QUESTION
If half of the sum of the lengths of the edges of a cube is 48, what is the volume of the cube?
ANSWER SELECTION
(A) 8
(B) 64
(C) 128
(D) 512 (THIS IS CORRECT!)
(E) 576
ANSWER EXPLANATION
If half of the sum of the lengths of the edges is 48, then the sum of the lengths of the edges is 2(48) = 96. Now, if we count the edges of a cube, we will find that there are 12. So the length of each edge is 96/12, or 8. The volume of a cube is the length of an edge cubed. The volume of this cube is 8^3 = 8 x 8 x 8 = 64 x 8 = 512 . Choice (D) is correct.
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