1972 AMC 12 Problem 12

Attempt Problem 12 of the 1972 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1972 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

12.

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:
66
864864
17281728
6×17286\times1728
23042304
Answer: B
Concepts:cube geometrysurface areavolumeunit conversion
Small hint:
If the edge is ff feet, its length in inches is 12f12f
Big hint:
Equate the numerical values f3f^3 and 6(12f)26(12f)^2
Solution:
Let the edge length be ff feet, or 12f12f inches. The stated numerical equality is f3=6(12f)2. f^3=6(12f)^2. Since f>0,f\gt0, division by f2f^2 gives f=6⋅144=864. f=6\cdot144=864.
Therefore, the correct answer is B.
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