Bunuel wrote:

If the volume of the cube above is 64 cubic centimeters, what is the shortest distance, in centimeters, from point A to point B?

A. \(4\sqrt{2}\)

B. \(4\sqrt{3}\)

C. \(4\sqrt{6}\)

D. \(8\sqrt{2}\)

E. \(8\sqrt{3}\)

Attachment:

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We'll go for Precise since there is an explicit rule that addresses this question.

This doesn't come up too often, but the diagonal of a cube has length \(\sqrt{3}a\), where a is the length of the side.

Since the volume is 64, then the length of each side is 4 (as 4^3=64) so the length of the diagonal is \(4\sqrt{3}\)

(B) is our answer.

Note - to calculate this, you need to use the Pythagorean theorem twice - once to find the diagonal of the side and the second time to find the diagonal of the cube.

The general equation for the diagonal of a rectangular solid is \(\sqrt{a^2+b^2+c^2}\) where a,b,c are the lengths of the sides.

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