2009 Cayley Problem 10

The front of a rectangular prism has an area of 12 cm^2, the side has an area of 6 cm^2, and the top has area 8 cm^2. The volume of the prism in cm^3, is

\textbf{(A)}\ 24\quad \textbf{(B)}\ 26\quad \textbf{(C)}\ 48\quad \textbf{(D)}\ 72\quad \textbf{(E)}\ 52

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.