Question

Consider a cube that measures 1 inch on each side. We can think of a cubic foot as a dilation of the

cubic inch by a factor of 12.
What is the volume, in cubic inches, of a cubic foot?
___in ³

Answer 1

1728 in³

Explanation:

You want the volume in cubic inches of a cubic foot.

Volume

The volume of a cube is equal to the cube of its edge dimension. The cube with edge 12 inches will have a volume of ...

V = s³

V = (12 in)³ = 1728 in³

A cubic foot is a volume of 1728 cubic inches.

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Additional comment

Perhaps this illustrates for you why the volume varies as the cube of the dilation factor. 1 in³ × 12³ = (12 in)³ = 1728 in³