AMC 8 1992 Problem 24

AMC8 1992 年第 24 题

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Four circles of radius 3 are arranged as shown. Their centers are the vertices of a square. The area of the shaded region is closest to

四个半径为 3 的圆如图所示排列。它们的圆心是一个正方形的顶点。着色区域的面积最接近

正确答案 · Correct Answer

解析 · Solution

Solution 1

The side of the square of made up of two radii, and the area of the square is

(3+3)^2=36

. The unshaded region of the square is composed of four quarter circles, and has the area of one circle, which is

9\pi

. The area of the shaded region is

36-9\pi

which less than 36-9(3)=9, closest to

\text{(A)7.7}

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