GRE Math : How to find the length of an edge of a cube
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Example Questions
Example Question #1 : How To Find The Length Of An Edge Of A Cube
Quantity A: The length of a side of a cube with a volume of 
Quantity B: The length of a side of a cube with surface area of 
Which of the following is true?
Quantity A is larger.
Quantity B is larger.
The relationship between the two quantities cannot be determined.
The two quantities are equal
The two quantities are equal
Recall that the equation for the volume of a cube is:
Since the sides of a cube are merely squares, the surface area equation is just 
So, for our two quantities:
Quantity A
Use your calculator to estimate this value (since you will not have a square root key). This is 
Quantity B
First divide by 
Therefore,
Therefore, the two quantities are equal.
Example Question #2 : Cubes
What is the length of an edge of a cube with a surface area of 
The surface area of a cube is made up of 
For our data, we know:
This means that:
Now, while you will not have a calculator with a square root key, you do know that 
Example Question #1 : Cubes
If a cube has a total surface area of 
There is not enough information given.
There are 6 sides to a cube. If the total surface area is 54 square inches, then each face must have an area of 9 square inches.
Every face of a cube is a square, so if the area is 9 square inches, each edge must be 3 inches.
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