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7 changes: 4 additions & 3 deletions source/calculus/source/06-AI/05.ptx
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<activity xml:id="activity-A4pyramidmass">
<introduction>
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.

<p>
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.
</p>
</introduction>

<task>
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<activity xml:id="activity-TI4pyramidcentermass">
<statement>
<p>
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.
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.
</p>
<p>
Use <xref ref="fact-AI4centerofmass"/> to find the height where the center of mass occurs.
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