3650.31 – Volume and Surface Area of a Cube

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

  1. 6 feet

  2. 864 feet

  3. 1,728 feet

  4. 10,368 feet

  5. 2,304 feet

Solution

If one edge of the cube is ss feet, then

Volume=s3 ft3, \text{Volume} = s^3 \text{ ft}^3,

while,

Surface Area=6s2 ft2=6s2⋅144 in2=864s2 in2. \text{Surface Area} = 6s^2 \text{ ft}^2 = 6s^2 \cdot 144 \text{ in}^2 = 864s^2 \text{ in}^2.

This means, according to the given, i.e., ignoring the miss-matched units,

s3=864s2⇝s=864.s^3 = 864s^2 \leadsto s = 864.

The correct answer is b. That's a pretty big cube. Would it fit on a soccer field?