Bunuel wrote:

What is the length, in centimeters, of an edge of a cube whose surface area is k square centimeters and whose volume is k/2 cubic centimeters?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 36

Volume of cube =\(\frac{k}{2}\) \(cm^3\)

Surface area of cube = \(6s^2 = k\) \(cm^2\)

Surface area to find side in terms of \(k\)\(6s^2 = k\)

\(s^2 = \frac{k}{6}\)

\(s = \frac{\sqrt{k}}{\sqrt{6}}\)

Volume to find numeric value of \(k\)Volume =\(\frac{k}{2}\) \(cm^3\)

\((\frac{\sqrt{k}}{\sqrt{6}})^3 = \frac{k}{2}\)

\(\sqrt{k} * \sqrt{k} * \sqrt{k} = k\sqrt{k}\)

\(\sqrt{6} * \sqrt{6} * \sqrt{6} = 6\sqrt{6}\)

\(\frac{k\sqrt{k}}{6\sqrt{6}} = \frac{k}{2}\)

\(2(k)\sqrt{k} = (k)6\sqrt{6}\)

\(\sqrt{k} = 3\sqrt{6}\)

\((\sqrt{k})^2 = (3\sqrt{6})^2\)

\(k = 54\)

Surface area to find side length of cubeSurface area of cube = \(6s^2 = k\) \(cm^2\)

\(6s^2 = 54\)

\(s^2 = 9\)

\(s = 3\) \(cm\)

I think

Answer A
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