fozzzy wrote:

If a certain cube has Volume V and a second cube has twice the surface area of the first cube, what is the volume of the second cube in terms of V?

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

B. \(2\sqrt{2}V\)

C. 2V

D. 4V

E. 8V

Since the first cube has a volume of V, V = s^3, where s = the side of the cube; thus, s = ∛V.

Since a cube has 6 faces, the surface area of the first cube is 6(∛V)^2 and thus the surface area of the second cube, which is twice that of the first cube, is 12(∛V)^2.

We can let S = the side of the second cube; thus:

6S^2 = 12(∛V)^2

S^2 = 2(∛V)^2

S = √2 * ∛V

Therefore, the volume of the second cube is S^3 = (√2 * ∛V)^3 = (√2)^3 * V = (√2)^2 * √2 * V = 2√2V.

Answer: B

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