Question

图中每个小圆的半径都是一。最里面的圆与围绕它的六个圆相切，这六个圆中的每个又与大圆以及相邻的小圆相切。求阴影区域的面积。

Each of the small circles in the figure has radius one. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find the area of the shaded region.

$\pi$

$1.5\pi$

$2\pi$

$3\pi$

$3.5\pi$

答案：C

知识点：相切圆圆面积

难度评级：1060

解答：

外圈小圆的圆心到中心的距离为 $2$ ，再加上它自己的半径 $1$ ，得到大圆半径为 $3$ 。

大圆面积为 $9\pi$ ，七个单位圆总面积为 $7\pi$ ，所以阴影面积为 $9\pi-7\pi=2\pi$ 。

所以正确答案是 C。

The center of a surrounding circle is $2$ from the center (two radii), and adding its own radius $1$ gives a large radius of $3.$

The large circle has area $9\pi,$ and the seven unit circles have total area $7\pi,$ so the shaded region is $9\pi-7\pi=2\pi.$

Thus, the correct answer is C.

2002 AMC 10A 第 5 题

答案：C

难度评级：1060

解答：

其他年份的第 5 题