In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 1 square unit, then what is the area of the shaded region, in square units?

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.