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Question

# A container in the shape of a right circular cylinder is 12 full of water. If the volume of water in the container is 36 cubic inches and the height of the container is 9 inches, what is the diameter of the base of the cylinder, in inches?

A
169π
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B
4π
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C
12pi
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D
2π
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E
42π
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Solution

## The correct option is E 4√2πFor a right cylinder, volume=π(radius)2(height). Since the volume of water is 36 cubic inches and since this represents 12 the container, the is occupying 12 the container's height, or 9(12)=4.5 inches. Let r be the radius of the cylinder.36=πr2(4.5)8=πr2 divide both sides by 4.58π=r2 divide both sides by π√8π=r take the square root of both sides2√2√π=r simplify the √8 to get the radiusThen, since the diameter is twice the length of the radius, the diameter equals2(2√2√π)=4√2√pi=4√2π.The correct answer is E.

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