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## Official Guide Explanation:Problem Solving #189

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: 189
Page: 179
Difficulty: 7 (Very Difficult)
Category 1: Word Problems > Geometry Problems >
Category 2: Geometry > Rectangular Solids and Cylinders > Cylinders
Category 3: Geometry > Rectangular Solids and Cylinders > Rectangular Solids

Explanation: The volume of a cylinder is given by π r2h, and in this question, there are three possible cylinders that could fit inside the box. There are three different sized - faced that the base of the cylinder could sit on: 6x8, 8x10, and 6x10. Recognize that in order to create the largest cylinder, we don't want space to go to waste, so the 6x10 face wouldn't be best: the circle could only have a diameter of 6. That leaves two other possibilities.

(1) If the base sits on the 6x8 face, then r = 3 and h = 10: π r2h= π 32(10) = 90 π

(2) if the base sits on the 8x10 face, then r = 4 and h = 6: π r2h= π 42(6) = 16(6) π =96 π

So, the cylinder with the largest volume is (2), meaning that the radius is 4, choice (B).

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