Official Guide Explanation:
Problem Solving #D22

Background

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Solution and Metadata

Question: D22
Page: 23
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Geometry Problems >
Category 2: Geometry > Rectangular Solids and Cylinders > Cylinders

Explanation: The volume of water in the cylinder is 36 cubic inches, but the cylinder is only half full, so the capacity of the container must be double that: 72 cubic inches. We know the height of the container is 9 inches, so we can use the formula for volume to calculate the radius of the base:

v= π r²h

72= π r²(9)

(8/( π )) = r²

r= rt[(8/( π ))]

We're looking for the diameter, which is twice the radius:

d = 2r = 2( rt[(8/( π ))])

d = 2(((2 rt[2])/( rt[ π ]))) = 4 rt[(2/( π ))], choice (E).

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