Other Polyhedrons - SAT Math

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Question

The above image is a silo made from two right circular cones, and a right circular cylinder where the dimensions are given in feet. Of the following answers, which one best represents the volume of the entire silo in cubic feet?

Answer

To solve this, we need to break it down into three parts.

$V_{\text{silo}}=V_{\text{cylinder}}+V_{\text{cone 1}}+V_{\text{cone 2}}$

$V_{\text{cylinder}}=\pi r^2h=\pi(3)^2\cdot12=108\pi$

$V_{\text{cone 1}}=\pi r^2\frac{h}{3}=\pi(3^2)\cdot \frac{4}{3}=12\pi$

$V_{\text{cone 2}}=\pi r^2\frac{h}{3}=\pi(3^2)\cdot \frac{4}{3}=12\pi$

$V_{\text{Silo}}=108\pi+12\pi+12\pi=132\pi$

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