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

1951 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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1951 AHSME Problems/Problem 6

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