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CAPS-Maths-Grade-11-7-Measurement.html
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<h2> <a href="maths.html"> ⇦ Back to the Maths chapter list</a></h2>
<section class="sv-section">
<h1>Measurement</h1>
<section class="sv-section">
<h2>1. Area of a polygon</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id1223-5278">ID is: 1223 Seed is: 5278<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Area formulae and algebra</h3>
</span><div class="multi-part"><ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p> Find an expression for the area of this figure in terms of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="mi" id="MathJax-Span-3" style="font-family: STIXGeneral; font-style: italic;">π₯</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-1"> x </script></span> . One side of the square is labelled <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-4" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.58em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-5"><span class="mn" id="MathJax-Span-6" style="font-family: STIXGeneral;">3</span><span class="mi" id="MathJax-Span-7" style="font-family: STIXGeneral; font-style: italic;">π₯</span><span class="mo" id="MathJax-Span-8" style="font-family: STIXGeneral; padding-left: 0.237em;">β</span><span class="mn" id="MathJax-Span-9" style="font-family: STIXGeneral; padding-left: 0.237em;">1</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>x</mi><mo>β</mo><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-2"> 3 x - 1 </script></span>.</span> Write your answer in expanded form (not factorised). </p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1223/5278/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0" width="300" height="300"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-10" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-11"><span class="mi" id="MathJax-Span-12" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-13" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-3"> A = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="9 x^2 - 6 x + 1" size="20"> <div class="response-type">polynomial</div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p> Find an expression for the area of this figure in terms of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-14" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-15"><span class="mi" id="MathJax-Span-16" style="font-family: STIXGeneral; font-style: italic;">π₯</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-4"> x </script></span> . The dimensions of the figure are labelled <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>x</mi><mo>&#x2212;</mo><mn>1</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-17" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.58em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-18"><span class="mn" id="MathJax-Span-19" style="font-family: STIXGeneral;">3</span><span class="mi" id="MathJax-Span-20" style="font-family: STIXGeneral; font-style: italic;">π₯</span><span class="mo" id="MathJax-Span-21" style="font-family: STIXGeneral; padding-left: 0.237em;">β</span><span class="mn" id="MathJax-Span-22" style="font-family: STIXGeneral; padding-left: 0.237em;">1</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mi>x</mi><mo>β</mo><mn>1</mn></math></span></span><script type="math/tex" id="MathJax-Element-5"> 3 x - 1 </script></span> and <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mi>x</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-23" style="width: 1.291em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.057em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-24"><span class="mn" id="MathJax-Span-25" style="font-family: STIXGeneral;">5</span><span class="mi" id="MathJax-Span-26" style="font-family: STIXGeneral; font-style: italic;">π₯</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-6"> 5 x </script></span>.</span> Write your answer in expanded form (not factorised). </p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1223/5278/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1" width="300" height="300"></a></div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-27" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-28"><span class="mi" id="MathJax-Span-29" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-30" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-7"> A = </script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="15 x^2 - 5 x" size="20"> <div class="response-type">polynomial</div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:25.166786"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id1223-559">ID is: 1223 Seed is: 559<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Area formulae and algebra</h3>
</span><div class="multi-part"><ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p> Find an expression for the area of this figure in terms of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-31" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-32"><span class="mi" id="MathJax-Span-33" style="font-family: STIXGeneral; font-style: italic;">π₯</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-8"> x </script></span> . One side of the square is labelled <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-34" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.7em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-35"><span class="mn" id="MathJax-Span-36" style="font-family: STIXGeneral;">2</span><span class="mi" id="MathJax-Span-37" style="font-family: STIXGeneral; font-style: italic;">π₯</span><span class="mo" id="MathJax-Span-38" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mn" id="MathJax-Span-39" style="font-family: STIXGeneral; padding-left: 0.237em;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></math></span></span><script type="math/tex" id="MathJax-Element-9"> 2 x + 4 </script></span>.</span> Write your answer in expanded form (not factorised). </p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1223/559/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(1)" width="300" height="300"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-40" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-41"><span class="mi" id="MathJax-Span-42" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-43" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-10"> A = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="4 x^2 + 16 x + 16" size="20"> <div class="response-type">polynomial</div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p> Find an expression for the area of this figure in terms of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-44" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-45"><span class="mi" id="MathJax-Span-46" style="font-family: STIXGeneral; font-style: italic;">π₯</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-11"> x </script></span> . The dimensions of the figure are labelled <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-47" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.7em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-48"><span class="mn" id="MathJax-Span-49" style="font-family: STIXGeneral;">2</span><span class="mi" id="MathJax-Span-50" style="font-family: STIXGeneral; font-style: italic;">π₯</span><span class="mo" id="MathJax-Span-51" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mn" id="MathJax-Span-52" style="font-family: STIXGeneral; padding-left: 0.237em;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></math></span></span><script type="math/tex" id="MathJax-Element-12"> 2 x + 4 </script></span> and <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x2212;</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-53" style="width: 4.16em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.399em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.4em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-54"><span class="mo" id="MathJax-Span-55" style="font-family: STIXGeneral;">β</span><span class="mn" id="MathJax-Span-56" style="font-family: STIXGeneral;">3</span><span class="mi" id="MathJax-Span-57" style="font-family: STIXGeneral; font-style: italic;">π₯</span><span class="mo" id="MathJax-Span-58" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mn" id="MathJax-Span-59" style="font-family: STIXGeneral; padding-left: 0.237em;">2</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>β</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn></math></span></span><script type="math/tex" id="MathJax-Element-13"> - 3 x + 2 </script></span>.</span> Write your answer in expanded form (not factorised). </p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1223/559/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(1)" width="300" height="300"></a></div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-60" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-61"><span class="mi" id="MathJax-Span-62" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-63" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-14"> A = </script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="-6 x^2 - 8 x + 8" size="20"> <div class="response-type">polynomial</div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:25.206643"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1240-3471">ID is: 1240 Seed is: 3471<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Area formulae for the basic shapes</h3>
</span><div class="problem">
<p>
For each of the shapes shown below, identify the correct formula for the <strong>area</strong> of the shape.
</p>
<table border="2">
<tbody><tr>
<td style="vertical-align:middle;background:#DDD;"> <strong>Shape A</strong> </td>
<td style="vertical-align:middle;background:#DDD;"> <strong>Shape B</strong> </td>
</tr>
<tr>
<td style="vertical-align:middle"> <div class="figure"><a href="https://www.emas.com/practice/isolated_image/1240/3471/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(2)" width="200" height="200"></a></div> </td>
<td style="vertical-align:middle"> <div class="figure"><a href="https://www.emas.com/practice/isolated_image/1240/3471/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(2)" width="200" height="200"></a></div> </td>
</tr>
</tbody></table>
<table border="1">
<tbody><tr>
<td align="center" style="vertical-align:middle;background:#DDD;"> <strong>Choice</strong> </td>
<td style="vertical-align:middle;background:#DDD;"> <strong>Area Formula</strong> </td>
</tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 1 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>b</mi><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-64" style="width: 3.691em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.989em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-65"><span class="mi" id="MathJax-Span-66" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-67" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mi" id="MathJax-Span-68" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π</span><span class="mi" id="MathJax-Span-69" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>b</mi><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-15"> A = b h </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 2 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-70" style="width: 4.16em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.399em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.4em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-71"><span class="mi" id="MathJax-Span-72" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-73" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mi" id="MathJax-Span-74" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-75"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-76" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-77"><span class="mrow" id="MathJax-Span-78"><span class="mn" id="MathJax-Span-79" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-16"> A = \pi r^{2} </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 3 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msup><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-80" style="width: 3.516em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.872em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-81"><span class="mi" id="MathJax-Span-82" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-83" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="msubsup" id="MathJax-Span-84" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 0.881em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.47em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-85" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.471em;"><span class="texatom" id="MathJax-Span-86"><span class="mrow" id="MathJax-Span-87"><span class="mn" id="MathJax-Span-88" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msup><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-17"> A = b^{2} </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 4 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mi>h</mi></mrow><mn>2</mn></mfrac></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-89" style="width: 3.75em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.047em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.05em, 3.106em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-90"><span class="mi" id="MathJax-Span-91" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-92" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mfrac" id="MathJax-Span-93" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.34em, 1000.71em, 4.16em, -999.997em); top: -4.388em; left: 50%; margin-left: -0.348em;"><span class="mrow" id="MathJax-Span-94"><span class="mi" id="MathJax-Span-95" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-96" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.34em, 1000.35em, 4.16em, -999.997em); top: -3.569em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-97" style="font-size: 70.7%; font-family: STIXGeneral;">2</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.82em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.823em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.568em; border-left: 0px solid; width: 0px; height: 1.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mi>h</mi></mrow><mn>2</mn></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-18"> A = \frac{b h}{2} </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 5 </td> <td> None of the above </td> </tr>
</tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>Shape A: <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">1</option><option value="1">2</option><option value="2" selected="">3</option><option value="3">4</option><option value="4">5</option></select> <br> <br> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mspace width="1em" /><mspace width="2em" /><mspace width="thickmathspace" /></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-98" style="width: 4.453em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.633em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.994em, 1003.63em, 2.345em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-99"><span class="mspace" id="MathJax-Span-100" style="height: 0em; vertical-align: 0em; width: 1.115em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-101" style="height: 0em; vertical-align: 0em; width: 2.228em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-102" style="height: 0em; vertical-align: 0em; width: 0.296em; display: inline-block; overflow: hidden;"></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mspace width="1em"></mspace><mspace width="2em"></mspace><mspace width="thickmathspace"></mspace></math></span></span><script type="math/tex" id="MathJax-Element-19">\quad \qquad \; </script></span> Shape B: <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">1</option><option value="1">2</option><option value="2">3</option><option value="3">4</option><option value="4">5</option></select></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:25.265988"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1240-9030">ID is: 1240 Seed is: 9030<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Area formulae for the basic shapes</h3>
</span><div class="problem">
<p>
For each of the shapes shown below, identify the correct formula for the <strong>area</strong> of the shape.
</p>
<table border="2">
<tbody><tr>
<td style="vertical-align:middle;background:#DDD;"> <strong>Shape A</strong> </td>
<td style="vertical-align:middle;background:#DDD;"> <strong>Shape B</strong> </td>
</tr>
<tr>
<td style="vertical-align:middle"> <div class="figure"><a href="https://www.emas.com/practice/isolated_image/1240/9030/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(3)" width="200" height="200"></a></div> </td>
<td style="vertical-align:middle"> <div class="figure"><a href="https://www.emas.com/practice/isolated_image/1240/9030/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(3)" width="200" height="200"></a></div> </td>
</tr>
</tbody></table>
<table border="1">
<tbody><tr>
<td align="center" style="vertical-align:middle;background:#DDD;"> <strong>Choice</strong> </td>
<td style="vertical-align:middle;background:#DDD;"> <strong>Area Formula</strong> </td>
</tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 1 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mi>h</mi><mn>2</mn></mfrac><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-103" style="width: 6.736em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.506em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1005.45em, 3.106em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-104"><span class="mi" id="MathJax-Span-105" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-106" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mfrac" id="MathJax-Span-107" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.34em, 1000.35em, 4.16em, -999.997em); top: -4.388em; left: 50%; margin-left: -0.173em;"><span class="mi" id="MathJax-Span-108" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">β</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.34em, 1000.35em, 4.16em, -999.997em); top: -3.569em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-109" style="font-size: 70.7%; font-family: STIXGeneral;">2</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.47em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.471em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span><span class="mrow" id="MathJax-Span-110"><span class="mo" id="MathJax-Span-111" style="font-family: STIXGeneral;">(</span><span class="mi" id="MathJax-Span-112" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mo" id="MathJax-Span-113" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mi" id="MathJax-Span-114" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.237em;">π</span><span class="mo" id="MathJax-Span-115" style="font-family: STIXGeneral;">)</span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.568em; border-left: 0px solid; width: 0px; height: 1.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><mi>h</mi><mn>2</mn></mfrac><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-20"> A = \frac{h}{2} \left(a + b\right) </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 2 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>b</mi><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-116" style="width: 3.691em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.989em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.93em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-117"><span class="mi" id="MathJax-Span-118" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-119" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mi" id="MathJax-Span-120" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π</span><span class="mi" id="MathJax-Span-121" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>b</mi><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-21"> A = b h </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 3 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-122" style="width: 4.16em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.399em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.4em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-123"><span class="mi" id="MathJax-Span-124" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-125" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mi" id="MathJax-Span-126" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-127"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-128" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-129"><span class="mrow" id="MathJax-Span-130"><span class="mn" id="MathJax-Span-131" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-22"> A = \pi r^{2} </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 4 </td> <td> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msup><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-132" style="width: 3.516em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.872em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-133"><span class="mi" id="MathJax-Span-134" style="font-family: STIXGeneral; font-style: italic;">π΄</span><span class="mo" id="MathJax-Span-135" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="msubsup" id="MathJax-Span-136" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 0.881em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.47em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-137" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.471em;"><span class="texatom" id="MathJax-Span-138"><span class="mrow" id="MathJax-Span-139"><span class="mn" id="MathJax-Span-140" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msup><mi>b</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-23"> A = b^{2} </script></span> </td> </tr>
<tr> <td align="center" style="vertical-align:middle;background:#DDD;"> 5 </td> <td> None of the above </td> </tr>
</tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>Shape A: <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">1</option><option value="1" selected="">2</option><option value="2">3</option><option value="3">4</option><option value="4">5</option></select> <br> <br> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mspace width="1em" /><mspace width="2em" /><mspace width="thickmathspace" /></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-141" style="width: 4.453em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.633em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.994em, 1003.63em, 2.345em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-142"><span class="mspace" id="MathJax-Span-143" style="height: 0em; vertical-align: 0em; width: 1.115em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-144" style="height: 0em; vertical-align: 0em; width: 2.228em; display: inline-block; overflow: hidden;"></span><span class="mspace" id="MathJax-Span-145" style="height: 0em; vertical-align: 0em; width: 0.296em; display: inline-block; overflow: hidden;"></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mspace width="1em"></mspace><mspace width="2em"></mspace><mspace width="thickmathspace"></mspace></math></span></span><script type="math/tex" id="MathJax-Element-24">\quad \qquad \; </script></span> Shape B: <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">1</option><option value="1">2</option><option value="2">3</option><option value="3" selected="">4</option><option value="4">5</option></select></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:25.290423"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1258-2407">ID is: 1258 Seed is: 2407<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Area calculations</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
Find the area of the shape shown for each of the three questions below.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answers to <strong>two decimal places</strong> if necessary. Do not type units into the answer box - just give the number.
</div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
<strong>Shape 1:</strong>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1258/2407/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(4)" width="260" height="255"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-146" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-147"><span class="mo" id="MathJax-Span-148" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-25"> = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="132" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-149" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-150"><span class="mrow" id="MathJax-Span-151"><span class="mtext" id="MathJax-Span-152" style="font-family: STIXGeneral;">m</span><span class="texatom" id="MathJax-Span-153"><span class="mrow" id="MathJax-Span-154"><span class="msubsup" id="MathJax-Span-155"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-156"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-157"><span class="mrow" id="MathJax-Span-158"><span class="mn" id="MathJax-Span-159" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-26">\text{m$^{2}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
<strong>Shape 2:</strong>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1258/2407/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(4)" width="196" height="196"></a></div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-160" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-161"><span class="mo" id="MathJax-Span-162" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-27"> = </script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="254,47" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>cm</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-163" style="width: 1.994em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1001.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-164"><span class="mrow" id="MathJax-Span-165"><span class="mtext" id="MathJax-Span-166" style="font-family: STIXGeneral;">cm</span><span class="texatom" id="MathJax-Span-167"><span class="mrow" id="MathJax-Span-168"><span class="msubsup" id="MathJax-Span-169"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-170"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-171"><span class="mrow" id="MathJax-Span-172"><span class="mn" id="MathJax-Span-173" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>cm</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-28">\text{cm$^{2}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
<strong>Shape 3:</strong>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1258/2407/2"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/2" width="285" height="274"></a></div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-174" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-175"><span class="mo" id="MathJax-Span-176" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-29"> = </script></span> <input name="question3a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="252,15" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-177" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-178"><span class="mrow" id="MathJax-Span-179"><span class="mtext" id="MathJax-Span-180" style="font-family: STIXGeneral;">m</span><span class="texatom" id="MathJax-Span-181"><span class="mrow" id="MathJax-Span-182"><span class="msubsup" id="MathJax-Span-183"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-184"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-185"><span class="mrow" id="MathJax-Span-186"><span class="mn" id="MathJax-Span-187" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-30">\text{m$^{2}$}</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.noerror)</div></div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:25.314999"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id1258-1562">ID is: 1258 Seed is: 1562<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Area calculations</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
Find the area of the shape shown for each of the three questions below.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answers to <strong>two decimal places</strong> if necessary. Do not type units into the answer box - just give the number.
</div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
<strong>Shape 1:</strong>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1258/1562/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(5)" width="305" height="250"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-188" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-189"><span class="mo" id="MathJax-Span-190" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-31"> = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="210" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-191" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-192"><span class="mrow" id="MathJax-Span-193"><span class="mtext" id="MathJax-Span-194" style="font-family: STIXGeneral;">m</span><span class="texatom" id="MathJax-Span-195"><span class="mrow" id="MathJax-Span-196"><span class="msubsup" id="MathJax-Span-197"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-198"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-199"><span class="mrow" id="MathJax-Span-200"><span class="mn" id="MathJax-Span-201" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-32">\text{m$^{2}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
<strong>Shape 2:</strong>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1258/1562/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(5)" width="184" height="184"></a></div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-202" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-203"><span class="mo" id="MathJax-Span-204" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-33"> = </script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="113,1" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-205" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-206"><span class="mrow" id="MathJax-Span-207"><span class="mtext" id="MathJax-Span-208" style="font-family: STIXGeneral;">m</span><span class="texatom" id="MathJax-Span-209"><span class="mrow" id="MathJax-Span-210"><span class="msubsup" id="MathJax-Span-211"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-212"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-213"><span class="mrow" id="MathJax-Span-214"><span class="mn" id="MathJax-Span-215" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-34">\text{m$^{2}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
<strong>Shape 3:</strong>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1258/1562/2"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/2(1)" width="290" height="274"></a></div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-216" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-217"><span class="mo" id="MathJax-Span-218" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-35"> = </script></span> <input name="question3a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="266,98" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-219" style="width: 1.467em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.174em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1001.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-220"><span class="mrow" id="MathJax-Span-221"><span class="mtext" id="MathJax-Span-222" style="font-family: STIXGeneral;">m</span><span class="texatom" id="MathJax-Span-223"><span class="mrow" id="MathJax-Span-224"><span class="msubsup" id="MathJax-Span-225"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-226"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-227"><span class="mrow" id="MathJax-Span-228"><span class="mn" id="MathJax-Span-229" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-36">\text{m$^{2}$}</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.noerror)</div></div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:25.336749"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section></section> <section class="sv-section">
<h2>2. Right prisms and cylinders</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id1222-8889">ID is: 1222 Seed is: 8889<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Surface area: triangular prisms</h3>
</span><div class="problem">
<p>The figure here is a triangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-230" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-231"><span class="mtext" id="MathJax-Span-232" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-37">\text{5}</script></span> units; the triangles, which are both right triangles, have sides which are <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-233" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-234"><span class="mtext" id="MathJax-Span-235" style="font-family: STIXGeneral;">2</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math></span></span><script type="math/tex" id="MathJax-Element-38">\text{2}</script></span>, <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4,58</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-236" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-237"><span class="mtext" id="MathJax-Span-238" style="font-family: STIXGeneral;">4,58</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4,58</mtext></math></span></span><script type="math/tex" id="MathJax-Element-39">\text{4,58}</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-239" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-240"><span class="mtext" id="MathJax-Span-241" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-40">\text{5}</script></span> units long. Determine the surface area of the figure. Round to two decimal places if necessary. (NOTE: The diagram is not necessarily drawn to scale.)</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1222/8889/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(6)" width="420" height="315"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface Area = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="67,06" size="10"> units<sup>2</sup>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.471693"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1222-3351">ID is: 1222 Seed is: 3351<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Surface area: triangular prisms</h3>
</span><div class="problem">
<p>The figure here is a triangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-242" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-243"><span class="mtext" id="MathJax-Span-244" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-41">\text{11}</script></span> units; the triangles, which are both right triangles, have sides which are <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5,66</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-245" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-246"><span class="mtext" id="MathJax-Span-247" style="font-family: STIXGeneral;">5,66</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5,66</mtext></math></span></span><script type="math/tex" id="MathJax-Element-42">\text{5,66}</script></span>, <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-248" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-249"><span class="mtext" id="MathJax-Span-250" style="font-family: STIXGeneral;">7</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>7</mtext></math></span></span><script type="math/tex" id="MathJax-Element-43">\text{7}</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-251" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-252"><span class="mtext" id="MathJax-Span-253" style="font-family: STIXGeneral;">9</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math></span></span><script type="math/tex" id="MathJax-Element-44">\text{9}</script></span> units long. Find the surface area of the figure. Round to two decimal places if necessary. (NOTE: The diagram is not necessarily drawn to scale.)</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1222/3351/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(7)" width="525" height="455"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface Area = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="277,88" size="10"> units<sup>2</sup>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.492850"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1241-1522">ID is: 1241 Seed is: 1522<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Volume: triangular prisms</h3>
</span><div class="problem">
<p>
The figure here is a triangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-254" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-255"><span class="mtext" id="MathJax-Span-256" style="font-family: STIXGeneral;">9</span><span class="mtext" id="MathJax-Span-257" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-258" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-45">\text{9} \ \text{units}</script></span>. The triangles both contain right angles, and have a side of length <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-259" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-260"><span class="mtext" id="MathJax-Span-261" style="font-family: STIXGeneral;">2</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2</mtext></math></span></span><script type="math/tex" id="MathJax-Element-46">\text{2}</script></span>, a side of length <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4,58</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-262" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-263"><span class="mtext" id="MathJax-Span-264" style="font-family: STIXGeneral;">4,58</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4,58</mtext></math></span></span><script type="math/tex" id="MathJax-Element-47">\text{4,58}</script></span> and a side of length <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-265" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-266"><span class="mtext" id="MathJax-Span-267" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-268" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-269" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-48">\text{5} \ \text{units}</script></span>.
</p>
<p>
Find the volume of the figure.
</p>
<div class="note"><span class="note-header">NOTE:</span>
The diagram is not necessarily drawn to scale.
</div>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1241/1522/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(8)" width="455" height="385"></a></div>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round to two decimal places if necessary.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
Volume <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-270" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-271"><span class="mo" id="MathJax-Span-272" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-49">=</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="41,22" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-273" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-274"><span class="mrow" id="MathJax-Span-275"><span class="mtext" id="MathJax-Span-276" style="font-family: STIXGeneral;">units</span><span class="texatom" id="MathJax-Span-277"><span class="mrow" id="MathJax-Span-278"><span class="msubsup" id="MathJax-Span-279"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-280"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-281"><span class="mrow" id="MathJax-Span-282"><span class="mn" id="MathJax-Span-283" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-50">\text{units$^{3}$}</script></span>
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.518874"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1241-4765">ID is: 1241 Seed is: 4765<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Volume: triangular prisms</h3>
</span><div class="problem">
<p>
The figure here is a triangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-284" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-285"><span class="mtext" id="MathJax-Span-286" style="font-family: STIXGeneral;">9</span><span class="mtext" id="MathJax-Span-287" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-288" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-51">\text{9} \ \text{units}</script></span>. The triangles both contain right angles, and have a side of length <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-289" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-290"><span class="mtext" id="MathJax-Span-291" style="font-family: STIXGeneral;">3</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>3</mtext></math></span></span><script type="math/tex" id="MathJax-Element-52">\text{3}</script></span>, a side of length <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-292" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-293"><span class="mtext" id="MathJax-Span-294" style="font-family: STIXGeneral;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math></span></span><script type="math/tex" id="MathJax-Element-53">\text{4}</script></span> and a side of length <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-295" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-296"><span class="mtext" id="MathJax-Span-297" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-298" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-299" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-54">\text{5} \ \text{units}</script></span>.
</p>
<p>
Find the volume of the figure.
</p>
<div class="note"><span class="note-header">NOTE:</span>
The diagram is not necessarily drawn to scale.
</div>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1241/4765/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(9)" width="420" height="385"></a></div>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round to two decimal places if necessary.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
Volume <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-300" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-301"><span class="mo" id="MathJax-Span-302" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-55">=</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="54" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-303" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-304"><span class="mrow" id="MathJax-Span-305"><span class="mtext" id="MathJax-Span-306" style="font-family: STIXGeneral;">units</span><span class="texatom" id="MathJax-Span-307"><span class="mrow" id="MathJax-Span-308"><span class="msubsup" id="MathJax-Span-309"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-310"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-311"><span class="mrow" id="MathJax-Span-312"><span class="mn" id="MathJax-Span-313" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-56">\text{units$^{3}$}</script></span>
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1247-7367">ID is: 1247 Seed is: 7367<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Volume: rectangular prisms</h3>
</span><div class="problem">
<p>
The figure here is a rectangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-314" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-315"><span class="mtext" id="MathJax-Span-316" style="font-family: STIXGeneral;">12</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext></math></span></span><script type="math/tex" id="MathJax-Element-57">\text{12}</script></span> units; the other dimensions of the prism are <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-317" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-318"><span class="mtext" id="MathJax-Span-319" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-58">\text{11}</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-320" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-321"><span class="mtext" id="MathJax-Span-322" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-59">\text{6}</script></span> units. Determine the volume of the figure. (NOTE: The diagram is not necessarily drawn to scale.)
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1247/7367/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(10)" width="650" height="400"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Volume = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="792" size="10"> units<sup>3</sup>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.567886"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1247-2402">ID is: 1247 Seed is: 2402<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Volume: rectangular prisms</h3>
</span><div class="problem">
<p>
The figure here is a rectangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-323" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-324"><span class="mtext" id="MathJax-Span-325" style="font-family: STIXGeneral;">5</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext></math></span></span><script type="math/tex" id="MathJax-Element-60">\text{5}</script></span> units; the other dimensions of the prism are <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-326" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-327"><span class="mtext" id="MathJax-Span-328" style="font-family: STIXGeneral;">9</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext></math></span></span><script type="math/tex" id="MathJax-Element-61">\text{9}</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-329" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-330"><span class="mtext" id="MathJax-Span-331" style="font-family: STIXGeneral;">4</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>4</mtext></math></span></span><script type="math/tex" id="MathJax-Element-62">\text{4}</script></span> units. Determine the volume of the figure. (NOTE: The diagram is not necessarily drawn to scale.)
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1247/2402/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(11)" width="550" height="225"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Volume = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="180" size="10"> units<sup>3</sup>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.587014"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1237-4816">ID is: 1237 Seed is: 4816<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Surface area: rectangular prisms</h3>
</span><div class="problem">
<p>
The figure here is a rectangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-332" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-333"><span class="mtext" id="MathJax-Span-334" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-63">\text{8}</script></span> units; the other dimensions of the prism are <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-335" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-336"><span class="mtext" id="MathJax-Span-337" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-64">\text{6}</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>14</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-338" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-339"><span class="mtext" id="MathJax-Span-340" style="font-family: STIXGeneral;">14</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>14</mtext></math></span></span><script type="math/tex" id="MathJax-Element-65">\text{14}</script></span> units. Calculate the surface area of the figure. (NOTE: The diagram is not necessarily drawn to scale.)
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1237/4816/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(12)" width="400" height="300"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface Area = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="488" size="10"> units<sup>2</sup>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.607312"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1237-3607">ID is: 1237 Seed is: 3607<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Surface area: rectangular prisms</h3>
</span><div class="problem">
<p>
The figure here is a rectangular prism. The height of the prism is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-341" style="width: 1.232em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.998em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-342"><span class="mtext" id="MathJax-Span-343" style="font-family: STIXGeneral;">11</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>11</mtext></math></span></span><script type="math/tex" id="MathJax-Element-66">\text{11}</script></span> units; the other dimensions of the prism are <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-344" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-345"><span class="mtext" id="MathJax-Span-346" style="font-family: STIXGeneral;">6</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>6</mtext></math></span></span><script type="math/tex" id="MathJax-Element-67">\text{6}</script></span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-347" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-348"><span class="mtext" id="MathJax-Span-349" style="font-family: STIXGeneral;">8</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>8</mtext></math></span></span><script type="math/tex" id="MathJax-Element-68">\text{8}</script></span> units. Calculate the surface area of the figure. (NOTE: The diagram is not necessarily drawn to scale.)
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1237/3607/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(13)" width="400" height="375"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface Area = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="404" size="10"> units<sup>2</sup>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.626218"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1245-4521">ID is: 1245 Seed is: 4521<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Volume: cylinders</h3>
</span><div class="problem">
<p>
The picture below shows a cylinder. The height of the cylinder is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-350" style="width: 3.926em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.223em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-351"><span class="mtext" id="MathJax-Span-352" style="font-family: STIXGeneral;">12</span><span class="mtext" id="MathJax-Span-353" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-354" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-69">\text{12}\ \text{units}</script></span>;</span> the radius of the cylinder is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>8</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-355" style="width: 5.389em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.394em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-356"><span class="mi" id="MathJax-Span-357" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mo" id="MathJax-Span-358" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-359" style="font-family: STIXGeneral; padding-left: 0.296em;">8</span><span class="mtext" id="MathJax-Span-360" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-361" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>8</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-70"> r = \text{8}\ \text{units}</script></span>.</span> The diagram is not necessarily drawn to scale. Find the volume of the figure.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1245/4521/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(14)" width="440" height="440"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Volume = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="2 412,74" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-362" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-363"><span class="mrow" id="MathJax-Span-364"><span class="mtext" id="MathJax-Span-365" style="font-family: STIXGeneral;">units</span><span class="texatom" id="MathJax-Span-366"><span class="mrow" id="MathJax-Span-367"><span class="msubsup" id="MathJax-Span-368"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-369"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-370"><span class="mrow" id="MathJax-Span-371"><span class="mn" id="MathJax-Span-372" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-71">\text{units$^{3}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.645917"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1245-9750">ID is: 1245 Seed is: 9750<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Volume: cylinders</h3>
</span><div class="problem">
<p>
The picture below shows a cylinder. The height of the cylinder is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-373" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-374"><span class="mtext" id="MathJax-Span-375" style="font-family: STIXGeneral;">5</span><span class="mtext" id="MathJax-Span-376" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-377" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>5</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-72">\text{5}\ \text{units}</script></span>;</span> the radius of the cylinder is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>5</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-378" style="width: 5.389em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.394em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-379"><span class="mi" id="MathJax-Span-380" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mo" id="MathJax-Span-381" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-382" style="font-family: STIXGeneral; padding-left: 0.296em;">5</span><span class="mtext" id="MathJax-Span-383" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-384" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>5</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-73"> r = \text{5}\ \text{units}</script></span>.</span> The diagram is not necessarily drawn to scale. Find the volume of the figure.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1245/9750/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(15)" width="240" height="240"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Volume = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="392,7" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-385" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-386"><span class="mrow" id="MathJax-Span-387"><span class="mtext" id="MathJax-Span-388" style="font-family: STIXGeneral;">units</span><span class="texatom" id="MathJax-Span-389"><span class="mrow" id="MathJax-Span-390"><span class="msubsup" id="MathJax-Span-391"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-392"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-393"><span class="mrow" id="MathJax-Span-394"><span class="mn" id="MathJax-Span-395" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-74">\text{units$^{3}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1246-2067">ID is: 1246 Seed is: 2067<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">3D objects: names and nets</h3>
</span><div class="problem">
<p>
Consider the object below.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1246/2067/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(16)" width="290" height="290"></a></div>
<ol>
<li>
What is the name of the object?
</li>
<li>
Choose the most correct net of the object.
</li>
</ol>
<div class="note"><span class="note-header">NOTE:</span>
The nets are not to scale.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<strong>1.</strong> Name: <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">rectangular prism</option><option value="2">block</option><option value="1">cube</option><option value="3">square pyramid</option></select>
</p>
<p>
<strong>2.</strong>
</p>
<div class="sv-radio-button-group" name="radio-question1b"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bA" name="question1b" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bA"><span class="sv-radio-button__label-heading">A</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(6)" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bB" name="question1b" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bB"><span class="sv-radio-button__label-heading">B</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/2(2)" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bC" name="question1b" type="radio" value="2" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bC"><span class="sv-radio-button__label-heading">C</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/3" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bD" name="question1b" type="radio" value="3"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bD"><span class="sv-radio-button__label-heading">D</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/4" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1b" type="radio" value=""></div></li></ul></div>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.686534"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1246-1184">ID is: 1246 Seed is: 1184<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">3D objects: names and nets</h3>
</span><div class="problem">
<p>
Consider the object below.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1246/1184/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(17)" width="290" height="290"></a></div>
<ol>
<li>
What is the name of the object?
</li>
<li>
Choose the most correct net of the object.
</li>
</ol>
<div class="note"><span class="note-header">NOTE:</span>
The nets are not to scale.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<strong>1.</strong> Name: <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="3">cube</option><option value="1">triangular pyramid</option><option value="2">triangular prism</option><option value="0" selected="">square pyramid</option></select>
</p>
<p>
<strong>2.</strong>
</p>
<div class="sv-radio-button-group" name="radio-question1b"><ul class="sv-list"><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bA"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bA" name="question1b" type="radio" value="0"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bA"><span class="sv-radio-button__label-heading">A</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(7)" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bB"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bB" name="question1b" type="radio" value="1"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bB"><span class="sv-radio-button__label-heading">B</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/2(3)" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bC"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bC" name="question1b" type="radio" value="2"><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bC"><span class="sv-radio-button__label-heading">C</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/3(1)" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item"><div class="sv-radio-button sv-radio-button--block-label" id="radio-node-1bD"><div class="sv-radio-button__input-faux"><input autocomplete="off" class="sv-radio-button__input" id="radio-button-1bD" name="question1b" type="radio" value="3" checked=""><span class="sv-radio-button__box"></span></div><label class="sv-radio-button__label" for="radio-button-1bD"><span class="sv-radio-button__label-heading">D</span><span class="sv-radio-button__label-body">
<div class="figure"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/4(1)" width="220" height="220"></div>
</span></label></div></li><li class="sv-list-item" style="display:none;"><div class="sv-radio-button"><input id="hidden" name="question1b" type="radio" value=""></div></li></ul></div>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.707768"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4352-8411">ID is: 4352 Seed is: 8411<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Aerosol can: volume & surface area of cylinder & sphere</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
A cylindrical aerosol can has a lid in the shape of a hemisphere that fits exactly on top of the can. The height of the can is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>14</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-396" style="width: 3.047em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.462em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-397"><span class="mtext" id="MathJax-Span-398" style="font-family: STIXGeneral;">14</span><span class="mtext" id="MathJax-Span-399" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-400" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>14</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-75">\text{14}\ \text{cm}</script></span> and the radius of the base of the can is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,0</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-401" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-402"><span class="mtext" id="MathJax-Span-403" style="font-family: STIXGeneral;">2,0</span><span class="mtext" id="MathJax-Span-404" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-405" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,0</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-76">\text{2,0}\ \text{cm}</script></span>.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4352/8411/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(18)"></a></div>
<div class="quote">
<p>
<strong>Volume and surface area formulas:</strong>
</p>
<ul>
<li>Volume of sphere <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>3</mn></mfrac></mstyle><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-406" style="width: 3.926em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.223em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.998em, 1003.22em, 3.399em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-407"><span class="mo" id="MathJax-Span-408" style="font-family: STIXGeneral;">=</span><span class="mstyle" id="MathJax-Span-409" style="padding-left: 0.296em;"><span class="mrow" id="MathJax-Span-410"><span class="mfrac" id="MathJax-Span-411"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.106em, 1000.47em, 4.16em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.231em;"><span class="mn" id="MathJax-Span-412" style="font-family: STIXGeneral;">4</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.106em, 1000.41em, 4.16em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.231em;"><span class="mn" id="MathJax-Span-413" style="font-family: STIXGeneral;">3</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.65em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.647em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span><span class="mi" id="MathJax-Span-414" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-415"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-416" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-417"><span class="mrow" id="MathJax-Span-418"><span class="mn" id="MathJax-Span-419" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.925em; border-left: 0px solid; width: 0px; height: 2.646em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>3</mn></mfrac></mstyle><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-77"> = \dfrac{4}{3}\pi r^{3}</script></span></li>
<li>Surface area of sphere <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-420" style="width: 3.516em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.872em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-421"><span class="mo" id="MathJax-Span-422" style="font-family: STIXGeneral;">=</span><span class="mn" id="MathJax-Span-423" style="font-family: STIXGeneral; padding-left: 0.296em;">4</span><span class="mi" id="MathJax-Span-424" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-425"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-426" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-427"><span class="mrow" id="MathJax-Span-428"><span class="mn" id="MathJax-Span-429" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-78"> = 4\pi r^{2}</script></span></li>
</ul>
</div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Calculate the surface area of the can with the lid in place as shown above.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-430" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-431"><span class="mo" id="MathJax-Span-432" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-79">=</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="213,63" size="10"> <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">cm</option><option value="1" selected="">cmΒ²</option><option value="2">cmΒ³</option></select>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
If the lid is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>40</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-433" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-434"><span class="mtext" id="MathJax-Span-435" style="font-family: STIXGeneral;">40</span><span class="mi" id="MathJax-Span-436" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>40</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-80">\text{40}\%</script></span> filled with liquid, as shown below, calculate the volume of the liquid in the lid.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4352/8411/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(8)"></a></div>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Volume of liquid <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-437" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-438"><span class="mo" id="MathJax-Span-439" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-81">=</script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="6,7" size="10"> <select name="question2b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">cm</option><option value="1">cmΒ²</option><option value="2" selected="">cmΒ³</option></select>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:26.775353"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id4352-1694">ID is: 4352 Seed is: 1694<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Aerosol can: volume & surface area of cylinder & sphere</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2015 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
A cylindrical aerosol can has a lid in the shape of a hemisphere that fits exactly on top of the can. The height of the can is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>17</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-440" style="width: 3.047em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.462em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-441"><span class="mtext" id="MathJax-Span-442" style="font-family: STIXGeneral;">17</span><span class="mtext" id="MathJax-Span-443" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-444" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>17</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-82">\text{17}\ \text{cm}</script></span> and the radius of the base of the can is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,9</mtext><mtext>&#xA0;</mtext><mtext>cm</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-445" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.7em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-446"><span class="mtext" id="MathJax-Span-447" style="font-family: STIXGeneral;">1,9</span><span class="mtext" id="MathJax-Span-448" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-449" style="font-family: STIXGeneral;">cm</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,9</mtext><mtext> </mtext><mtext>cm</mtext></math></span></span><script type="math/tex" id="MathJax-Element-83">\text{1,9}\ \text{cm}</script></span>.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4352/1694/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(19)"></a></div>
<div class="quote">
<p>
<strong>Volume and surface area formulas:</strong>
</p>
<ul>
<li>Volume of sphere <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>3</mn></mfrac></mstyle><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-450" style="width: 3.926em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.223em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.998em, 1003.22em, 3.399em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-451"><span class="mo" id="MathJax-Span-452" style="font-family: STIXGeneral;">=</span><span class="mstyle" id="MathJax-Span-453" style="padding-left: 0.296em;"><span class="mrow" id="MathJax-Span-454"><span class="mfrac" id="MathJax-Span-455"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.106em, 1000.47em, 4.16em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.231em;"><span class="mn" id="MathJax-Span-456" style="font-family: STIXGeneral;">4</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.106em, 1000.41em, 4.16em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.231em;"><span class="mn" id="MathJax-Span-457" style="font-family: STIXGeneral;">3</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.65em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.647em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span><span class="mi" id="MathJax-Span-458" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-459"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-460" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-461"><span class="mrow" id="MathJax-Span-462"><span class="mn" id="MathJax-Span-463" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.925em; border-left: 0px solid; width: 0px; height: 2.646em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>3</mn></mfrac></mstyle><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-84"> = \dfrac{4}{3}\pi r^{3}</script></span></li>
<li>Surface area of sphere <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-464" style="width: 3.516em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.872em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-465"><span class="mo" id="MathJax-Span-466" style="font-family: STIXGeneral;">=</span><span class="mn" id="MathJax-Span-467" style="font-family: STIXGeneral; padding-left: 0.296em;">4</span><span class="mi" id="MathJax-Span-468" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-469"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-470" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-471"><span class="mrow" id="MathJax-Span-472"><span class="mn" id="MathJax-Span-473" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-85"> = 4\pi r^{2}</script></span></li>
</ul>
</div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Calculate the surface area of the can with the lid in place as shown above.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface area <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-474" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-475"><span class="mo" id="MathJax-Span-476" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-86">=</script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="236,97" size="10"> <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">cm</option><option value="1" selected="">cmΒ²</option><option value="2">cmΒ³</option></select>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
If the lid is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>80</mtext><mi mathvariant="normal">&#x0025;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-477" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.7em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-478"><span class="mtext" id="MathJax-Span-479" style="font-family: STIXGeneral;">80</span><span class="mi" id="MathJax-Span-480" style="font-family: STIXGeneral;">%</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>80</mtext><mi mathvariant="normal">%</mi></math></span></span><script type="math/tex" id="MathJax-Element-87">\text{80}\%</script></span> filled with liquid, as shown below, calculate the volume of the liquid in the lid.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4352/1694/1"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/1(9)"></a></div>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Volume of liquid <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-481" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-482"><span class="mo" id="MathJax-Span-483" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-88">=</script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="11,49" size="10"> <select name="question2b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">cm</option><option value="1">cmΒ²</option><option value="2" selected="">cmΒ³</option></select>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:26.845480"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id1221-8818">ID is: 1221 Seed is: 8818<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Surface area: cylinders</h3>
</span><div class="problem">
<p>
A cylinder is shown below. The height of the cylinder is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-484" style="width: 3.282em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.696em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-485"><span class="mtext" id="MathJax-Span-486" style="font-family: STIXGeneral;">9</span><span class="mtext" id="MathJax-Span-487" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-488" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>9</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-89">\text{9}\ \text{units}</script></span>; the radius of the cylinder is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>4</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-489" style="width: 5.389em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.394em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-490"><span class="mi" id="MathJax-Span-491" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mo" id="MathJax-Span-492" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-493" style="font-family: STIXGeneral; padding-left: 0.296em;">4</span><span class="mtext" id="MathJax-Span-494" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-495" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>4</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-90"> r = \text{4}\ \text{units}</script></span>,</span> as shown. The diagram is not necessarily drawn to scale. Calculate the surface area of the figure.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1221/8818/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(20)" width="225" height="225"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface Area = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="326,73" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-496" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-497"><span class="mrow" id="MathJax-Span-498"><span class="mtext" id="MathJax-Span-499" style="font-family: STIXGeneral;">units</span><span class="texatom" id="MathJax-Span-500"><span class="mrow" id="MathJax-Span-501"><span class="msubsup" id="MathJax-Span-502"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-503"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-504"><span class="mrow" id="MathJax-Span-505"><span class="mn" id="MathJax-Span-506" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-91">\text{units$^{2}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.881250"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id1221-596">ID is: 1221 Seed is: 596<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST">
<span class="worked_example"><h3 class="sv-heading">Surface area: cylinders</h3>
</span><div class="problem">
<p>
A cylinder is shown below. The height of the cylinder is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-507" style="width: 3.926em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.223em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.16em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-508"><span class="mtext" id="MathJax-Span-509" style="font-family: STIXGeneral;">12</span><span class="mtext" id="MathJax-Span-510" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-511" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>12</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-92">\text{12}\ \text{units}</script></span>; the radius of the cylinder is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>7</mtext><mtext>&#xA0;</mtext><mtext>units</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-512" style="width: 5.389em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.394em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1004.34em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-513"><span class="mi" id="MathJax-Span-514" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mo" id="MathJax-Span-515" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-516" style="font-family: STIXGeneral; padding-left: 0.296em;">7</span><span class="mtext" id="MathJax-Span-517" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-518" style="font-family: STIXGeneral;">units</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mtext>7</mtext><mtext> </mtext><mtext>units</mtext></math></span></span><script type="math/tex" id="MathJax-Element-93"> r = \text{7}\ \text{units}</script></span>,</span> as shown. The diagram is not necessarily drawn to scale. Find the surface area of the figure.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to two decimal places.
</div>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/1221/596/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(21)" width="400" height="400"></a></div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Surface Area = <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="835,66" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-519" style="width: 2.872em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.345em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.35em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-520"><span class="mrow" id="MathJax-Span-521"><span class="mtext" id="MathJax-Span-522" style="font-family: STIXGeneral;">units</span><span class="texatom" id="MathJax-Span-523"><span class="mrow" id="MathJax-Span-524"><span class="msubsup" id="MathJax-Span-525"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-526"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-527"><span class="mrow" id="MathJax-Span-528"><span class="mn" id="MathJax-Span-529" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>units</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mrow></mrow></math></span></span><script type="math/tex" id="MathJax-Element-94">\text{units$^{2}$}</script></span>
<div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:04:26.903075"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4355-847">ID is: 4355 Seed is: 847<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Water tank: cylinder & cone volume</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
The diagram below shows a water tank which is made up of a cylinder and cone having equal radii. The height of the tank is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,9</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-530" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-531"><span class="mtext" id="MathJax-Span-532" style="font-family: STIXGeneral;">2,9</span><span class="mtext" id="MathJax-Span-533" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-534" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,9</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-95">\text{2,9}\ \text{m}</script></span> and the perpendicular height of the cone, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-535" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.47em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-536"><span class="mi" id="MathJax-Span-537" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span class="mi" id="MathJax-Span-538" style="font-family: STIXGeneral; font-style: italic;">π</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi></math></span></span><script type="math/tex" id="MathJax-Element-96">PQ</script></span>,</span> is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,8</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-539" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-540"><span class="mtext" id="MathJax-Span-541" style="font-family: STIXGeneral;">0,8</span><span class="mtext" id="MathJax-Span-542" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-543" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,8</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-97">\text{0,8}\ \text{m}</script></span>. The angle between the radius and the slant height, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>R</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-544" style="width: 1.818em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.467em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-545"><span class="mi" id="MathJax-Span-546" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span class="mi" id="MathJax-Span-547" style="font-family: STIXGeneral; font-style: italic;">π
</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>R</mi></math></span></span><script type="math/tex" id="MathJax-Element-98">PR</script></span>,</span> of the conical section, is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>39,7</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-548" style="width: 2.638em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.169em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-549"><span class="mtext" id="MathJax-Span-550" style="font-family: STIXGeneral;">39,7</span><span class="texatom" id="MathJax-Span-551"><span class="mrow" id="MathJax-Span-552"><span class="mo" id="MathJax-Span-553" style="font-family: STIXGeneral;">Β°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>39,7</mtext><mrow class="MJX-TeXAtom-ORD"><mo>Β°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-99">\text{39,7}Β°</script></span>.</span>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4355/847/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(22)"></a></div>
<div class="quote">
<p>
<strong>Volume and surface area formulas:</strong>
</p>
<ul>
<li>Volume of cone <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-100-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-554" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.52em, 3.106em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-555"><span class="mo" id="MathJax-Span-556" style="font-family: STIXGeneral;">=</span><span class="mfrac" id="MathJax-Span-557" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -4.388em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-558" style="font-size: 70.7%; font-family: STIXGeneral;">1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -3.569em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-559" style="font-size: 70.7%; font-family: STIXGeneral;">3</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.47em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.471em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span><span class="mi" id="MathJax-Span-560" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-561"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-562" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-563"><span class="mrow" id="MathJax-Span-564"><span class="mn" id="MathJax-Span-565" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mi" id="MathJax-Span-566" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.568em; border-left: 0px solid; width: 0px; height: 1.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-100"> = \frac{1}{3}\pi r^{2}h</script></span></li>
<li>Total surface area of cone <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-101-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>&#x03C0;</mi><mi>r</mi><mi>s</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-567" style="width: 6.033em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.921em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1004.86em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-568"><span class="mo" id="MathJax-Span-569" style="font-family: STIXGeneral;">=</span><span class="mi" id="MathJax-Span-570" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-571"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-572" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-573"><span class="mrow" id="MathJax-Span-574"><span class="mn" id="MathJax-Span-575" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-576" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mi" id="MathJax-Span-577" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.237em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-578" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-579" style="font-family: STIXGeneral; font-style: italic;">π </span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>Ο</mi><mi>r</mi><mi>s</mi></math></span></span><script type="math/tex" id="MathJax-Element-101"> = \pi r^{2} + \pi rs</script></span></li>
<li>Volume of cylinder <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-102-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-580" style="width: 3.516em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.872em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.81em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-581"><span class="mo" id="MathJax-Span-582" style="font-family: STIXGeneral;">=</span><span class="mi" id="MathJax-Span-583" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-584"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-585" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-586"><span class="mrow" id="MathJax-Span-587"><span class="mn" id="MathJax-Span-588" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mi" id="MathJax-Span-589" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-102"> = \pi r^{2}h</script></span></li>
<li>Total surface area of cylinder <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-103-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>&#x03C0;</mi><mi>r</mi><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-590" style="width: 7.321em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.975em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1005.92em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-591"><span class="mo" id="MathJax-Span-592" style="font-family: STIXGeneral;">=</span><span class="mn" id="MathJax-Span-593" style="font-family: STIXGeneral; padding-left: 0.296em;">2</span><span class="mi" id="MathJax-Span-594" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-595"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-596" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-597"><span class="mrow" id="MathJax-Span-598"><span class="mn" id="MathJax-Span-599" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-600" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mn" id="MathJax-Span-601" style="font-family: STIXGeneral; padding-left: 0.237em;">2</span><span class="mi" id="MathJax-Span-602" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-603" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-604" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>Ο</mi><mi>r</mi><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-103"> = 2\pi r^{2} + 2\pi r h</script></span></li>
</ul>
</div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
Calculate the radius, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-104-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>R</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-605" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.52em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-606"><span class="mi" id="MathJax-Span-607" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-608" style="font-family: STIXGeneral; font-style: italic;">π
</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>R</mi></math></span></span><script type="math/tex" id="MathJax-Element-104">QR</script></span>.</span>
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-105-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>R</mi><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-609" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.46em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-610"><span class="mi" id="MathJax-Span-611" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-612" style="font-family: STIXGeneral; font-style: italic;">π
</span><span class="mo" id="MathJax-Span-613" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>R</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-105">QR = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="0,96" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-106-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-614" style="width: 0.94em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.876em, 1000.76em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-615"><span class="mtext" id="MathJax-Span-616" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-106">\text{m}</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
When the tank is full, an electric pump switches on and pumps water from the tank into an irrigation system at a rate of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-107-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,86</mtext><mtext>&#xA0;</mtext><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow><mtext>/h</mtext></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-617" style="width: 4.862em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.984em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1003.98em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-618"><span class="mtext" id="MathJax-Span-619" style="font-family: STIXGeneral;">2,86</span><span class="mtext" id="MathJax-Span-620" style="font-family: STIXGeneral;"> </span><span class="mrow" id="MathJax-Span-621"><span class="mtext" id="MathJax-Span-622" style="font-family: STIXGeneral;">m</span><span class="texatom" id="MathJax-Span-623"><span class="mrow" id="MathJax-Span-624"><span class="msubsup" id="MathJax-Span-625"><span style="display: inline-block; position: relative; width: 0.413em; height: 0px;"><span style="position: absolute; clip: rect(3.809em, 1000em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-626"></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0em;"><span class="texatom" id="MathJax-Span-627"><span class="mrow" id="MathJax-Span-628"><span class="mn" id="MathJax-Span-629" style="font-size: 70.7%; font-family: STIXGeneral;">3</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span></span><span class="mtext" id="MathJax-Span-630" style="font-family: STIXGeneral;">/h</span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.361em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2,86</mtext><mtext> </mtext><mrow><mtext>m</mtext><mrow class="MJX-TeXAtom-ORD"><msup><mi></mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup></mrow><mtext>/h</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-107">\text{2,86}\ \text{m$^{3}$/h}</script></span>. The pump automatically switches off when the tank is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-108-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>6</mn></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-631" style="width: 1.115em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.881em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.647em, 1000.88em, 3.047em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-632"><span class="mstyle" id="MathJax-Span-633"><span class="mrow" id="MathJax-Span-634"><span class="mfrac" id="MathJax-Span-635"><span style="display: inline-block; position: relative; width: 0.647em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.106em, 1000.41em, 4.16em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.231em;"><span class="mn" id="MathJax-Span-636" style="font-family: STIXGeneral;">1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.106em, 1000.47em, 4.16em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.231em;"><span class="mn" id="MathJax-Span-637" style="font-family: STIXGeneral;">6</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.65em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.647em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.925em; border-left: 0px solid; width: 0px; height: 2.646em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>6</mn></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-108">\dfrac{1}{6}</script></span> full.
</p>
<p>
Calculate how long, in <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-109-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>hours</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-638" style="width: 2.755em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.228em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-639"><span class="mtext" id="MathJax-Span-640" style="font-family: STIXGeneral;">hours</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>hours</mtext></math></span></span><script type="math/tex" id="MathJax-Element-109">\text{hours}</script></span>, the pump feeds water into the irrigation system.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to the nearest <strong>half hour</strong>.
</div>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
Time taken <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-110-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-641" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.935em, 1000.65em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-642"><span class="mo" id="MathJax-Span-643" style="font-family: STIXGeneral;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.575em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-110">=</script></span> <input name="question2a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="2" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-111-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>hours</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-644" style="width: 2.755em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.228em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.17em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-645"><span class="mtext" id="MathJax-Span-646" style="font-family: STIXGeneral;">hours</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>hours</mtext></math></span></span><script type="math/tex" id="MathJax-Element-111">\text{hours}</script></span>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:04:27.007076"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id4355-460">ID is: 4355 Seed is: 460<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/e3f8824c-f082-5e5c-9e28-f43bc3768f0b" method="POST"><span class="worked_example"><h3 class="sv-heading">Water tank: cylinder & cone volume</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Nov 2016 Grade 11, P1, Q8</em></span><br>
<a url="/info/maths-formulae" href="https://www.emas.com/info/maths-formulae">Maths formulas</a>
</p>
<p>
The diagram below shows a water tank which is made up of a cylinder and cone having equal radii. The height of the tank is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-112-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,7</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-647" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-648"><span class="mtext" id="MathJax-Span-649" style="font-family: STIXGeneral;">1,7</span><span class="mtext" id="MathJax-Span-650" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-651" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1,7</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-112">\text{1,7}\ \text{m}</script></span> and the perpendicular height of the cone, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-113-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-652" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.47em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-653"><span class="mi" id="MathJax-Span-654" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span class="mi" id="MathJax-Span-655" style="font-family: STIXGeneral; font-style: italic;">π</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi></math></span></span><script type="math/tex" id="MathJax-Element-113">PQ</script></span>,</span> is <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-114-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,5</mtext><mtext>&#xA0;</mtext><mtext>m</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-656" style="width: 2.813em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.286em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.29em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-657"><span class="mtext" id="MathJax-Span-658" style="font-family: STIXGeneral;">0,5</span><span class="mtext" id="MathJax-Span-659" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-660" style="font-family: STIXGeneral;">m</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0,5</mtext><mtext> </mtext><mtext>m</mtext></math></span></span><script type="math/tex" id="MathJax-Element-114">\text{0,5}\ \text{m}</script></span>. The angle between the radius and the slant height, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-115-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>R</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-661" style="width: 1.818em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.467em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-662"><span class="mi" id="MathJax-Span-663" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span class="mi" id="MathJax-Span-664" style="font-family: STIXGeneral; font-style: italic;">π
</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>R</mi></math></span></span><script type="math/tex" id="MathJax-Element-115">PR</script></span>,</span> of the conical section, is <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-116-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>36,9</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-665" style="width: 2.638em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.169em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.11em, 2.813em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-666"><span class="mtext" id="MathJax-Span-667" style="font-family: STIXGeneral;">36,9</span><span class="texatom" id="MathJax-Span-668"><span class="mrow" id="MathJax-Span-669"><span class="mo" id="MathJax-Span-670" style="font-family: STIXGeneral;">Β°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.211em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>36,9</mtext><mrow class="MJX-TeXAtom-ORD"><mo>Β°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-116">\text{36,9}Β°</script></span>.</span>
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4355/460/0"><img src="./CAPS-Maths-Grade-11-7-Measurement_files/0(23)"></a></div>
<div class="quote">
<p>
<strong>Volume and surface area formulas:</strong>
</p>
<ul>
<li>Volume of cone <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-117-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-671" style="width: 4.394em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.574em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.467em, 1003.52em, 3.106em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-672"><span class="mo" id="MathJax-Span-673" style="font-family: STIXGeneral;">=</span><span class="mfrac" id="MathJax-Span-674" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -4.388em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-675" style="font-size: 70.7%; font-family: STIXGeneral;">1</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.34em, 1000.3em, 4.16em, -999.997em); top: -3.569em; left: 50%; margin-left: -0.173em;"><span class="mn" id="MathJax-Span-676" style="font-size: 70.7%; font-family: STIXGeneral;">3</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1000.47em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.471em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span><span class="mi" id="MathJax-Span-677" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-678"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-679" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-680"><span class="mrow" id="MathJax-Span-681"><span class="mn" id="MathJax-Span-682" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mi" id="MathJax-Span-683" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.568em; border-left: 0px solid; width: 0px; height: 1.718em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-117"> = \frac{1}{3}\pi r^{2}h</script></span></li>
<li>Total surface area of cone <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-118-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>&#x03C0;</mi><mi>r</mi><mi>s</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-684" style="width: 6.033em; display: inline-block;"><span style="display: inline-block; position: relative; width: 4.921em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1004.86em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-685"><span class="mo" id="MathJax-Span-686" style="font-family: STIXGeneral;">=</span><span class="mi" id="MathJax-Span-687" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-688"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-689" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-690"><span class="mrow" id="MathJax-Span-691"><span class="mn" id="MathJax-Span-692" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-693" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mi" id="MathJax-Span-694" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.237em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-695" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-696" style="font-family: STIXGeneral; font-style: italic;">π </span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi>Ο</mi><mi>r</mi><mi>s</mi></math></span></span><script type="math/tex" id="MathJax-Element-118"> = \pi r^{2} + \pi rs</script></span></li>
<li>Volume of cylinder <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-119-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-697" style="width: 3.516em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.872em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1002.81em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-698"><span class="mo" id="MathJax-Span-699" style="font-family: STIXGeneral;">=</span><span class="mi" id="MathJax-Span-700" style="font-family: STIXGeneral; font-style: italic; padding-left: 0.296em;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-701"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-702" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-703"><span class="mrow" id="MathJax-Span-704"><span class="mn" id="MathJax-Span-705" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mi" id="MathJax-Span-706" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-119"> = \pi r^{2}h</script></span></li>
<li>Total surface area of cylinder <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-120-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>&#x03C0;</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>&#x03C0;</mi><mi>r</mi><mi>h</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-707" style="width: 7.321em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.975em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.525em, 1005.92em, 2.755em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-708"><span class="mo" id="MathJax-Span-709" style="font-family: STIXGeneral;">=</span><span class="mn" id="MathJax-Span-710" style="font-family: STIXGeneral; padding-left: 0.296em;">2</span><span class="mi" id="MathJax-Span-711" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="msubsup" id="MathJax-Span-712"><span style="display: inline-block; position: relative; width: 0.823em; height: 0px;"><span style="position: absolute; clip: rect(3.34em, 1000.41em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-713" style="font-family: STIXGeneral; font-style: italic;">π</span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -4.33em; left: 0.413em;"><span class="texatom" id="MathJax-Span-714"><span class="mrow" id="MathJax-Span-715"><span class="mn" id="MathJax-Span-716" style="font-size: 70.7%; font-family: STIXGeneral;">2</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-717" style="font-family: STIXGeneral; padding-left: 0.237em;">+</span><span class="mn" id="MathJax-Span-718" style="font-family: STIXGeneral; padding-left: 0.237em;">2</span><span class="mi" id="MathJax-Span-719" style="font-family: STIXGeneral; font-style: italic;">π<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-720" style="font-family: STIXGeneral; font-style: italic;">π</span><span class="mi" id="MathJax-Span-721" style="font-family: STIXGeneral; font-style: italic;">β</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.139em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>Ο</mi><msup><mi>r</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>Ο</mi><mi>r</mi><mi>h</mi></math></span></span><script type="math/tex" id="MathJax-Element-120"> = 2\pi r^{2} + 2\pi r h</script></span></li>
</ul>
</div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>