SAT Math : How to find the length of an edge of a cube
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Example Question #1 : How To Find The Length Of An Edge Of A Cube
The number of square units in the surface area of a cube is twice as large as the number of cubic units in its volume. What is the cube's volume, in cubic units?
9
108
27
216
36
27
The number of square units in the surface area of a cube is given by the formula 6s2, where s is the length of the side of the cube in units. Moreover, the number of cubic units in a cube's volume is equal to s3.
Since the number of square units in the surface area is twice as large as the cubic units of the volume, we can write the following equation to solve for s:
6s2 = 2s3
Subtract 6s2 from both sides.
2s3 – 6s2 = 0
Factor out 2s2 from both terms.
2s2(s – 3) = 0
We must set each factor equal to zero.
2s2 = 0, only if s = 0; however, no cube has a side length of zero, so s can't be zero.
Set the other factor, s – 3, equal to zero.
s – 3 = 0
Add three to both sides.
s = 3
This means that the side length of the cube is 3 units. The volume, which we previously stated was equal to s3, must then be 33, or 27 cubic units.
The answer is 27.
Example Question #2 : Solid Geometry
You own a Rubik's cube with a volume of 
No enough information to solve.
You own a Rubik's cube with a volume of 
To solve for edge length, think of the volume of a cube formula:
Now, we have the volume, so just rearrange it to solve for side length:
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