Volume Equals Surface Area

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 in feet is:

  1. 6
  2. 864
  3. 1728
  4. 6 · 1728
  5. 2304


Show/Hide Solution

Let s represent the length of an edge in feet. Then:

Volume = s3 cubic feet.
The surface area is 6s2 square feet. There are 144 square inches in 1 square foot.
So the surface area is 6 · s2 · 144 = 864s2 square inches.
So s3 = 864s2 → s = 864 feet. The answer is (b).

Check:
V = 8643 = 644,972,544 cubic feet. An edge is 864 · 12 = 10,368 inches.
Surface area = 6 · 103682 = 644,972,544 square inches. Ok.

Leave a Reply

Your email address will not be published.