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## Official Guide Explanation:Problem Solving #D22

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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