15. As shown in Figure 4, the diameter of each small circle is equal to the radius of the large circle. If the sum of the areas of the two small circles is 1, then the shaded area is ( ).
(A) $\frac{1}{4}$
(B) $\frac{1}{3}$
(C) $\frac{1}{2}$
(D) 1
(E) $\frac{\pi}{2}$
15. D.

Let the radius of the large circle be $R$. Then the radius of the small circle is $\frac{R}{2}$. Since the ratio of the areas of the large circle to the small circle is the square of the ratio of their radii, the area of one small circle is $\frac{1}{4}$ of the area of the large circle, meaning the area of the large circle is twice the sum of the areas of two small circles. Therefore, the shaded area is equal to the sum of the areas of the two small circles, which is 1.