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.