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# What is the volume of a cube with edge e? (1) The value of

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Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
What is the volume of a cube with edge e? (1) The value of [#permalink]

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26 Nov 2010, 07:24
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Difficulty:

35% (medium)

Question Stats:

75% (01:32) correct 25% (00:59) wrong based on 12 sessions

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What is the volume of a cube with edge e?

(1) The value of e2 is 16.
(2) The ratio of the surface area of the cube to the volume of the cube is 3 : 2

can someone explain the OA to me
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 39755

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26 Nov 2010, 07:33
rxs0005 wrote:
What is the volume of a cube with edge e?

(1) The value of e2 is 16.
(2) The ratio of the surface area of the cube to the volume of the cube is 3 : 2

can someone explain the OA to me

The volume of a cube equals to $$volume_{cube}=e^3$$, where $$e$$ is the length of an edge. So all we need to find the volume is the value of $$e$$.

(1) The value of e2 is 16 --> $$e^2=16$$ --> $$e=4$$, (e=-4 is out as length can not be negative). Sufficient.

(2) The ratio of the surface area of the cube to the volume of the cube is 3 : 2 --> a cube has 6 faces and each has an area of $$e^2$$, so total surface are is $$6e^2$$. Now, we are told that $$\frac{6e^2}{e^3}=\frac{3}{2}$$ --> $$e=4$$. Sufficient.

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26 Nov 2010, 09:36
thanks i was confused whether we can actually get the value from the ratios in S2 the lesson learnt here is that if you are finally left with onevariable then its the value
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Re: Geometry DS   [#permalink] 26 Nov 2010, 09:36
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