In the diagram, $A B C D$ is a rectangle. If the area of the circle is equal to the area of the shaded region, the radius of the circle is
(A) $\sqrt{\frac{6}{\pi}}$
(B) $\frac{6}{\pi}$
(C) $\frac{6}{\sqrt{\pi}}$
(D) $\sqrt{\frac{18}{\pi}}$
(E) $\frac{18}{\pi}$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-105.jpg?height=350&width=463&top_left_y=2075&top_left_x=1297)
Since the areas of the circle and the shaded region are equal, then each is equal to half of the area of the entire rectangle, so each is equal to $\frac{1}{2}(8 \times 9)=36$.

If the radius of the circle is $r$, then $\pi r^{2}=36$, so $r^{2}=\frac{36}{\pi}$ or $r=\sqrt{\frac{36}{\pi}}=\frac{\sqrt{36}}{\sqrt{\pi}}=\frac{6}{\sqrt{\pi}}$.

ANSWER: (C)