如下图所示，2个小圆各自的直径都是大圆的半径，如果这2个小圆的面积之和是1平方单位，那么图中阴影部分的面积是多少平方单位？

A. $\frac{1}{4}$

B. $\frac{1}{3}$

C. $\frac{1}{2}$

D. 1

E. $\frac{\pi}{2}$

1. 2018 AMC 8 官方解析

Denote the radius of the big circle by $R$. Then the radius of the small circle is $\frac{R}{2}$. Since the area of a circle is in direct proportion to its squared radius, the ratio of the area of the small circle to the area of the big circle is $\frac{1}{4}$ , which means the combined area of the two small circles is half of the area of the big circle. Therefore, the area of the shaded region equals the combined area of the two small circles. Hence, the answer is D.