2002 Cayley Problem 24

A cylinder, which has a diameter of 27 and a height of 30, contains two lead spheres with radii 6 and 9, with the larger sphere sitting on the bottom of the cylinder, as shown. Water is poured into the cylinder so that it just covers both spheres. The volume of water required is

\textbf{(A)}\ 3672\pi\quad \textbf{(B)}\ 3660\pi\quad \textbf{(C)}\ 3375\pi\quad \textbf{(D)}\ 3114\pi\quad \textbf{(E)}\ 4374\pi

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.