GRE Math : How to find the length of an edge of a cube

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Cubes

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?

Possible Answers:

Quantity A is larger.

The relationship between the two quantities cannot be determined.

Quantity B is larger.

The two quantities are equal

Correct answer:

The two quantities are equal

Explanation:

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  times the area of one of those squares:

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 ?

Possible Answers:

Correct answer:

Explanation:

The surface area of a cube is made up of  squares. Therefore, the equation is merely  times the area of one of those squares.  Since the sides of a square are equal, this is:

, where  is the length of one side of the square.

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 . (You can always use your calculator to test values like this.) Therefore, we know that . This is the length of one side

Example Question #3 : Cubes

If a cube has a total surface area of  square inches, what is the length of one edge?

Possible Answers:

There is not enough information given.

 

Correct answer:

 

Explanation:

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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