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## Official Guide Explanation:Problem Solving #D05

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: D05
Page: 20
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Rectangular Solids and Cylinders > Cylinders
Category 2: Word Problems > Geometry Problems >

Explanation: There are two cylinders to consider here. First, the actual cylindrical tank. If the tank is half full and the water reaches a height of 4 feet, the height of the tank itself must be 8 feet. Second, the cylinder of water--that is, the half of the tank that is filled. If the water has a volume of 36 π and a height of 4, we can calculate the radius of the base:

v= π r2h

36 π = π r2(4)

9 = r2

r = 3

Thus, the tank has a radius of 3 feet.

Next, the tank is turned on its side. If the radius of the tank is 3 feet, the diameter of the tank is 6 feet, meaning that the "height" of the tank, now that it's lying on its side, is 6 feet. Since the tank is half full, the height of the water is now 3 feet, choice (B).

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