Official Guide Explanation:
Problem Solving #160




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Solution and Metadata

Question: 160
Page: 175
Difficulty: 5 (Moderate)
Category 1: Word Problems > Geometry Problems >
Category 2: Geometry > Circles > Multiple figures

Explanation: The easiest (perhaps the only reasonable) way to find the area of the path is to find the area of the inner (unshaded) circle and the area of the outer circle, then find the diffferent. The area of a circle is given by π r2, so since the inner circle's radius is 8, the area is 82 π =64 π . The path is 3 feet wide, so the radius of the larger circle is 8 + 3 = 11, so the outer circle's area is given by 112 π =121 π . The difference is 121 π -64 π =57 π , choice (D).

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