AHSME 1951 Problem 6

The bottom, side, and front areas of a rectangular box are known. The product of these areas is equal to: $\textbf{(A)}\ \text{the volume of the box} \textbf{(B)}\ \text{the square root of the volume} \textbf{(C)}\ \text{twice the volume}$ $\textbf{(D)}\ \text{the square of the volume} \textbf{(E)}\ \text{the cube of the volume}$