2010 AMC 10B Problem 16

A square of side length 1 and a circle of radius \dfrac{\sqrt{3}}{3} share the same center. What is the area inside the circle, but outside the square?

\textbf{(A)}\ \dfrac{\pi}{3}-1 \qquad \textbf{(B)}\ \dfrac{2\pi}{9}-\dfrac{\sqrt{3}}{3} \qquad \textbf{(C)}\ \dfrac{\pi}{18} \qquad \textbf{(D)}\ \dfrac{1}{4} \qquad \textbf{(E)}\ \dfrac{2\pi}{9}

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