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Question

# Determine the volume to the nearest cubic unit. cone r=20 in. h=25 in.

Solution

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The volume $V$ of a cone or a pyramid is the product of the base area $B$ and the height $h$.

$V=\frac{1}{3}Bh$

where $B$ is the base area and $h$ is the height of the cone or pyramid.

Given:

$d=20 \text{ \ in} \Rightarrow r=\frac{d}{2}=\frac{20}{2}=10 \text{ \ in}$

$h=25 \text{ \ in}$

Area of the circle is

$A=\pi r^2=\pi \left(\frac{d}{2}\right)^2$

where $r$ is the radius of the circle and $d$ is the diameter.

So,

$B=\pi r^2=\pi (10)^2=100 \pi \text{ \ in}^2 =100 \times 3.14 \approx 314 \text{ \ in}^2$

Hence,

$V=\frac{1}{3}Bh=\frac{1}{3} \times 314 \times 25 \text{ \ in}^3=2617 \text{ \ in}^3$

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