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What is the volume of a certain cube?

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What is the volume of a certain cube? [#permalink] New post 11 Aug 2014, 04:00
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What is the volume of a certain cube?

(1) The sum of the lengths of the edges of the cube is 36.

(2) The surface area of the cube is 54.
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Aug 2014, 01:23, edited 1 time in total.
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Re: What is the volume of a certain cube? [#permalink] New post 11 Aug 2014, 05:57
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joaomario wrote:
What is the volume of a certain cube?

(1) The sum of the lengths of the edges of the cube is 36.

(2) The surface area of the cube is 54.


For this question, you need to know:
1) A cube has 12 equal length sides, so sum of side length = 12 (length of one side)
2) surface area of a square = length x width (since length = width in a square) = length x length
3) A cube has 6 square faces with equal area, so sum of surface area = 6 (surface area of one side) = 6 (length x length)
4) volume of a cube = length x length x length

So, let's start with statement 1:

Sum of lengths = 36 = 12 (length of one side)
Using algebra, you know that length of one side = 3
Once you have length of one side, you know the volume of the cube. Therefore this is SUFFICIENT.

Eliminate B, C and E.

On to statement 2:
Total surface area = 54
Since there are 6 square faces: 54/6 = area for 1 face = 9
Since area of 1 face of square = 9 = length x length = 3x3
Length of one side = 3
Once you have length of one side, you know the volume of the cube. Therefore this is SUFFICIENT.

Correct answer D.
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Re: What is the volume of a certain cube? [#permalink] New post 11 Aug 2014, 20:39
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joaomario wrote:
What is the volume of a certain cube?

(1) The sum of the lengths of the edges of the cube is 36.

(2) The surface area of the cube is 54.


All you need to uniquely define a cube is any one measurement - length of a side/edge, area of a surface, volume etc. If you have any one of them, you can uniquely determine the others. So each statement alone is sufficient here.

To show how,

(1) The sum of the lengths of the edges of the cube is 36.
A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3
Volume = 3*3*3 = 27

(2) The surface area of the cube is 54.
A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)
6s^2 = 54
s = 3
Volume = 3*3*3 = 27

Answer (D)
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Re: What is the volume of a certain cube?   [#permalink] 11 Aug 2014, 20:39
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