AMC8 1992

AMC8 1992 · Q5

AMC8 1992 · Q5. It mainly tests Rounding & estimation, Area & perimeter.

A circle of diameter 1 is removed from a 2£3 rectangle, as shown. Which whole number is closest to the area of the shaded region?

从2×3矩形中移除一个直径为1的圆，如图所示。阴影区域的面积最接近哪个整数？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): The area of the circle is between 1/2 and 1. To see this, draw squares around and inside the circle. The area of the large square is 1, the area of the small square is 1/2, and the circle fits between the two squares. The area of the rectangle with the circle removed is therefore between 5 and 5.5, so the whole number closest to this area is 5.

答案（E）：圆的面积介于 $1/2$ 和 $1$ 之间。为说明这一点，在圆的外部和内部分别画一个正方形。大正方形的面积是 $1$，小正方形的面积是 $1/2$，而圆位于这两个正方形之间。因此，把圆从矩形中去掉后剩余部分的面积介于 $5$ 和 $5.5$ 之间，所以最接近该面积的整数是 $5$。

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