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What is the volume of the cube?

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Source: — Data Sufficiency |
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by pemdas » Sun Sep 09, 2012 4:51 pm
Striver wrote:What is the volume of the cube?

(1) The surface area of the cube is 600 square inches.

(2) The length of diagonal AB is 10√3.
st(1) implies 6a^2=600 or a=10 and we get a^3=1000 Suff
st(2) AB=Sqrt(A^2+B^2+C^2)=A*Sqrt(3)=10Sqrt(3), where A=10 and A^3=1000 Suff

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by Anurag@Gurome » Sun Sep 09, 2012 5:47 pm
Striver wrote:What is the volume of the cube?

(1) The surface area of the cube is 600 square inches.

(2) The length of diagonal AB is 10√3.
Let each side of the cube = s inches
Then volume = s^3

(1) The surface area of the cube is 600 square inches.
Surface area of cube = area of face * no. of faces
So, surface area of cube = s² * 6
s² * 6 = 600 implies s² = 100 or s = 10
Hence, volume = 10^3 = 1000; SUFFICIENT.

(2) The length of diagonal AB is 10√3.
Diagonal of cube = √(s² + s² + s²) = s√3
s√3 = 10√3 implies s = 10
So, volume = 10^3; SUFFICIENT.

The correct answer is D.
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