2010 AMC 8 Problem 16

A square and a circle have the same area. What is the ratio of the side length of the square to the radius of the circle?

\textbf{(A)}\ \frac{\sqrt{\pi}}{2} \qquad\textbf{(B)}\ \sqrt{\pi} \qquad\textbf{(C)}\ \pi \qquad\textbf{(D)}\ 2\pi \qquad\textbf{(E)}\ \pi^{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.