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xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="liter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="71" left="24" top="299.25" width="105" height="15.75" align-x="39.75" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14"> <b>Triangle Method</b> </f> </p> </text> </region> <region region-id="72" left="246" top="320.25" width="175.5" height="48" align-x="254.25" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <i>This does not work because a triangular </i> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <i>swept volume is not equivalent to half of a rectangular swept volume</i> </p> </text> </region> <region region-id="73" left="42" top="313.5" width="166.5" height="46.5" align-x="80.25" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="halfT2">V</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:id xml:space="preserve" 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<ml:plus/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="halfT2">V</ml:id> <ml:real>8</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">d</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="outer">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:real>0.2</ml:real> </ml:apply> <ml:id xml:space="preserve">in</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="inner">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.4906798138228989</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="liter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="76" left="30" top="428.25" width="95.25" height="12" align-x="42" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Swept Outer Volume: </p> </text> </region> <region region-id="79" left="144" top="423" width="153.75" height="22.5" align-x="178.5" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="outer">V</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>3.93</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="outer">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.066730589661649</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="liter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="81" left="30" top="452.25" width="89.25" height="12" align-x="39" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Swept Inner Volume:</p> </text> </region> <region region-id="83" left="144" top="447" width="152.25" height="22.5" align-x="177.75" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="inner">V</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>3.93</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="inner">r</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> 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