The diagonal of one face of a cube measures 42 inches . what is the volume of the cube?

The diagonal of one face of a cube measures 42 inches . what is the volume of the cube? Correct Answer 64 cbic inches

Let's call the length of each side of the cube 's'. Then the diagonal of one face is 4√2 inches. We can use the Pythagorean theorem to find the length of 's':s2 + s2 = (4√2)2 ⇒ 2s2 = 32 ⇒ s2 = 16 ∴ s = 4 inchesSo the volume of the cube is:V = s3 ⇒ V = 43 ∴ V = 64 cubic inches.
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