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A cube and a pyramid of square base share the same

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by BTGmoderatorLU » Mon Oct 08, 2018 3:35 pm

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B

C

D

E

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Source: EMPOWERgmat

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A cube and a pyramid of square base share the same dimensions: length, width, and height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216

The OA is D
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by Jay@ManhattanReview » Wed Oct 10, 2018 1:02 am
BTGmoderatorLU wrote:Source: EMPOWERgmat

Image

A cube and a pyramid of square base share the same dimensions: length, width, and height. If the volume of the cube is equal to the surface area of the cube, then what is the volume of the pyramid?

A. 9
B. 64/3
C. 27
D. 72
E. 216

The OA is D
Say the side of the cube = a, thus, the volume of the cube = a^3 and the surface area of the cube = 6a^2

=> a^3 = 6a^2 => a = 6

Note that the volume of a pyramid = Volume of cube/3

Volume of a pyramid = Volume of cube/3 = a^3/3 = 6^3/3 = 72

The correct answer: D

Hope this helps!

-Jay
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