What is the ratio of surface area to volume for a cube with a volume of 64 cubic inches?

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Answer 1 · 2015-07-04T16:05:41

The formula for the volume of a cube is

$V = a^3$ , where $a$ is the length of a side.

$a = root3V = root3("64 in"^3) = "4 in"$

Each face of the cube is a square.

$A = a^2 = ("4 in")^2 = "16 in"^2$

A cube has 6 faces, so the surface area of the cube is given by

$"SA" = 6 cancel("faces") × ("16 in"^2)/(1 cancel("face")) = "96 in"^2$

$"SA"/"V" = 96/64 = 1.5/1$