2004 Pascal Problem 22

A container in the shape of a cube has edge length 20 cm and contains some water. A solid gold cube, with edge length 15 cm, sinks to the bottom of this container, causing the water level to rise just to the top of the *solid* cube. Which of the following is closest to the original depth of the water?

\textbf{(A)}\ 6.56 \text{ cm}\quad \textbf{(B)}\ 8.25 \text{ cm}\quad \textbf{(C)}\ 10.50 \text{ cm}\quad \textbf{(D)}\ 5.31 \text{ cm}\quad \textbf{(E)}\ 7.50 \text{ cm}

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 Pascal contests here.