### All GMAT Math Resources

## Example Questions

### Example Question #1 : Calculating The Length Of An Edge Of A Cube

If the volume of a cube is units cubed, what is the length of each side of the cube?

**Possible Answers:**

**Correct answer:**

We solve for the side of the cube by deriving it from the volume of a cube formula:

### Example Question #2 : Cubes

If a cube has a surface area of , what is the length of one side?

**Possible Answers:**

**Correct answer:**

To find the surface area of a cube, use the following formula:

Where s is our side length.

Rearrange for s to get the following:

Plug in 54 for SA and solve

Don't forget your units, in this case centimeters so we get 3 centimeters

### Example Question #3 : Cubes

If a cube has a surface area of , what is the length of one of its sides?

**Possible Answers:**

**Correct answer:**

To solve for the side length of the cube, we need to use the formula for surface area. There are six faces on a cube, so its total surface area is just six times the area of one of its square faces, which is given by the side length squared:

### Example Question #4 : Cubes

If a cube has a volume of and is made up of smaller cubes, what is the length of one side of one of the smaller cubes?

**Possible Answers:**

**Correct answer:**

Volume of a cube is equal to the cube of its side. 343 is equal to 7 cubed, so the length of the whole cube is 7 cm. The cube is made up of 27 smaller cubes though. That means that one face of the cube is made up of 9 cubes and one edge of the whole cube is made up of 3 small cubes. That means that the length of one small cube is equal to the total length of one side divided by the numbers of cubes per side

Then we get our final answer by doing:

### Example Question #5 : Cubes

is a cube with diagonal . What is the length of an edge of the cube?

**Possible Answers:**

**Correct answer:**

We are given the length of the diagonal of the cube.

Therefore we can find the length of an edge by using the formula

or , and .

Therefore, the final answer is .

### Example Question #6 : Cubes

Find the length of the edge of a cube given that the volume is .

**Possible Answers:**

**Correct answer:**

To find side length, you must use the equation for volume of a cube and solve for .

Thus,

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