1951 AHSME Problems/Problem 6

Problem

The bottom, side, and front areas of a rectangular box are known. The product of these areas is equal to:

$\textbf{(A)}\ \text{the volume of the box} \qquad\textbf{(B)}\ \text{the square root of the volume} \qquad\textbf{(C)}\ \text{twice the volume}$ $\textbf{(D)}\ \text{the square of the volume} \qquad\textbf{(E)}\ \text{the cube of the volume}$

Solution

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. $\boxed{\textbf{(D)}}$

See Also

1951 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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