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SAT Math : How to find the volume of a polyhedron

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Example Question #1 : Other Polyhedrons

Screen shot 2016 02 19 at 8.45.22 am

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?

Possible Answers:

$108\pi$ $\displaystyle 108\pi$

$132\pi$ $\displaystyle 132\pi$

$24\pi$ $\displaystyle 24\pi$

$100\pi$ $\displaystyle 100\pi$

$120\pi$ $\displaystyle 120\pi$

Correct answer:

$132\pi$ $\displaystyle 132\pi$

Explanation:

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

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

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

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

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

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

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SAT Math : How to find the volume of a polyhedron

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Example Question #1 : Other Polyhedrons

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