AHSME 1973 Problem 25

A circular grass plot 12 feet in diameter is cut by a straight gravel path 3 feet wide, one edge of which passes through the center of the plot. The number of square feet in the remaining grass area is $\textbf{(A)}\ 36\pi-34 \textbf{(B)}\ 30\pi - 15 \textbf{(C)}\ 36\pi - 33$ $\textbf{(D)}\ 35\pi - 9\sqrt3 \textbf{(E)}\ 30\pi - 9\sqrt3$