1972 AHSME Problems/Problem 12

Problem

The number of cubic feet in the volume of a cube is the same as the number of square inches in its surface area. The length of the edge expressed as a number of feet is

$\textbf{(A) }6\qquad \textbf{(B) }864\qquad \textbf{(C) }1728\qquad \textbf{(D) }6\times 1728\qquad \textbf{(E) }2304$

Solution

If the side length of a cube is $s$ feet the volume is $s^3$ cubic feet and the surface area is $6(12s^2)$ square inches. The volume and surface are numerically equal, so we can write $s^3 = 6(12s^2)$ Solving yields $s=864.$

The answer is $\textbf{(B)}.$

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1972 AHSME Problems/Problem 12

Problem

Solution