Official Guide Explanation:
Problem Solving #189




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Solution and Metadata

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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