AMC8 2000

AMC8 2000 · Q19

AMC8 2000 · Q19. It mainly tests Circle theorems, Area & perimeter.

Three circular arcs of radius 5 units bound the region shown. Arcs AB and AD are quarter-circles, and arc BCD is a semi-circle. What is the area, in square units, of the region?

三个半径为5单位的圆弧包围了所示区域。弧AB和AD是四分之一圆，弧BCD是半圆。该区域面积有多少平方单位？

(A) 25 25

(B) $10 + 5\pi$ $10 + 5\pi$

(D) $50 + 5\pi$ $50 + 5\pi$

(E) $25\pi$ $25\pi$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Divide the semicircle in half and rotate each half down to fill the space below the quarter-circles. The figure formed is a rectangle with dimensions 5 and 10. The area is 50.

答案（C）：将半圆分成两半，并将每一半向下旋转以填充四分之一圆下方的空间。形成的图形是一个长为 10、宽为 5 的矩形。面积为 50。

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