Official Guide Explanation:
Problem Solving #D20




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Solution and Metadata

Question: D20
Page: 23
Difficulty: 7 (Very Difficult)
Category 1: Geometry > Circles > Multiple figures
Category 2: Geometry > Circles > other

Explanation: The toughest thing about this problem is visualizing the interaction between the two shapes. If the base of the hemisphere and the base of the cone coincide, they are equal. Since the cone is inscribed, it is as tall as the hemisphere. That is, the height of the cone is equal to the radius of the hemisphere. (The "height" of a hemisphere is equal to its radius.) Thus, the ratio of the height of the cone to the radius of the hemisphere is 1:1, since the two are equal. Choice (B) is correct.

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