The bottom, side, and front areas of a rectangular box are known. The product of these areas
is equal to:
$\textbf{(A)}\ \text{the volume of the box} \qquad\textbf{(B)}\ \text{the square root of the volume} \qquad\textbf{(C)}\ \text{twice the volume}$
$\textbf{(D)}\ \text{the square of the volume} \qquad\textbf{(E)}\ \text{the cube of the volume}$
Let the length of the edges of this box have lengths $a$, $b$, and $c$. We're given $ab$, $bc$, and $ca$. The product of these values is $a^2b^2c^2$, which is the square of the volume of the box. $\boxed{\textbf{(D)}}$