2009
Problem - 1540
A circle of radius $2$ is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?
The radius of the outer semi-circle is $4$, hence the area of the semi-circle is $8\pi$. The area of the circle is $4\pi$. Therefore, the answer is $$\frac{8\pi - 4\pi}{8\pi}=\boxed{\frac{1}{2}}$$