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Updated Activities 6.5.14 and 6.5.20. (#930)
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source/calculus/source/06-AI/05.ptx

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<activity xml:id="activity-A4pyramidmass">
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<introduction>
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Consider a pyramid with a <m>8\times 8</m> ft square base and a height of 16 feet. Suppose the density of the pyramid is <m>\delta(h)=10+\cos(\pi h)</m> lb/ft<m>^3</m> where <m>h</m> is the height in feet.
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<p>
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Consider a pyramid with an <m>8\times 8</m> ft square base and a height of 16 feet. Suppose the density of the pyramid is <m>\delta(h)=10+\cos(\pi h)</m> lb/ft<m>^3</m> where <m>h</m> is the height in feet.
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</p>
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</introduction>
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<task>
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<activity xml:id="activity-TI4pyramidcentermass">
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<statement>
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<p>
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Consider that for the pyramid from <xref ref="activity-A4pyramidmass"/>, a cross section of height <m>h</m> is <m>A(h)=\pi\cdot \left( \frac{16-h}{2}\right)^2</m> ft<m>^2</m>. Also recall that the density of the pyramid is <m>\delta(h)=10+\cos{\pi h}</m> lb/feet<m>^3</m>, where <m>h</m> is the height in feet, and that we found the total mass to be about 3414.14.6 lb.
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Consider that for the pyramid from <xref ref="activity-A4pyramidmass"/>, a cross section of height <m>h</m> is <m>A(h)=\left( \frac{16-h}{2}\right)^2</m> ft<m>^2</m>. Also recall that the density of the pyramid is <m>\delta(h)=10+\cos{\pi h}</m> lb/ft<m>^3</m>, where <m>h</m> is the height in feet, and that we found the total mass to be about 3414.14 lb.
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</p>
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<p>
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Use <xref ref="fact-AI4centerofmass"/> to find the height where the center of mass occurs.

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