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 
$\textbf{(A)}\ 36\pi-34 \qquad \textbf{(B)}\ 30\pi - 15 \qquad \textbf{(C)}\ 36\pi - 33 \qquad$
$\textbf{(D)}\ 35\pi - 9\sqrt3 \qquad \textbf{(E)}\ 30\pi - 9\sqrt3$
The wanted area can be divided into a semicircle and a circular segment.  The area of the semicircle is $\tfrac12 \cdot \pi \cdot 6^2 = 18\pi$ square feet.  To find the area of the circular segment, note that by using 30-60-90 triangles (or [Law of Cosines](https://artofproblemsolving.com/wiki/index.php/Law_of_Cosines)), the chord's length is $6\sqrt{3}$ ft, and the angle of the sector is $120^\circ$.  That means the area of the circular segment is $(\tfrac13 \cdot \pi \cdot 6^2) - (\tfrac12 \cdot 6\sqrt{3} \cdot 3) = 12\pi - 9\sqrt{3}$ square feet.  Thus, the area of the remaining grassy area is $\boxed{\textbf{(E)}\ 30\pi - 9\sqrt3}$ square feet.