How to find the length of an edge of a cube

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Geometry › How to find the length of an edge of a cube

Questions 1 - 10

1

If the surface area of a cube is , find the length of one side of the cube.

$6\sqrt2$

$8\sqrt3$

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{96}{6}}$

Simplify.

$\text{side length}=\sqrt{16}$

Reduce.

$\text{side length}=4$

2

If the surface area of a cube is , find the length of a side of the cube.

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{864}{6}}$

Simplify.

$\text{side length}=\sqrt{144}$

Reduce.

$\text{side length}=12$

3

If the surface area of a cube is , find the length of a side of the cube.

$5\sqrt5$

$4\sqrt2$

$7\sqrt7$

$6\sqrt6$

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{750}{6}}$

Simplify.

$\text{side length}=\sqrt{125}$

Reduce.

$\text{side length}=5\sqrt5$

4

If the surface area of a cube is , find the length of a side of the cube.

$2\sqrt7$

$7\sqrt3$

$6\sqrt3$

$10\sqrt2$

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{168}{6}}$

Simplify.

$\text{side length}=\sqrt{28}$

Reduce.

$\text{side length}=2\sqrt7$

5

The volume of a cube is .

Find the length of the cube to the nearest tenth of a foot.

Explanation

Since the volume of a cube is length times width times height, with every measurement being the same, we just need to take the cube root of the volume:

$^3\sqrt{43}=3.50$ .

Rounded to the nearest tenth, the length is 3.5 feet.

6

If the surface area of a cube is , find the length of one side of the cube.

$\sqrt{10}$

$4\sqrt3$

$2\sqrt6$

$6\sqrt2$

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{60}{6}}$

Simplify.

$\text{side length}=\sqrt{10}$

7

A cube has a volume of $512\hspace{1mm}m^3$ . What is the lengh of one of the edges of this cube?

$8\hspace{1mm} meters$

$9\hspace{1mm} meters$

$7\hspace{1mm} meters$

$6\hspace{1mm} meters$

$7.8\hspace{1mm}meters$

Explanation

Since cubes have side lengths that are equal and we find the volume by , then the side length of a cube with a volume of $512\hspace{1mm}m^3$ is simply $512\hspace{1mmm^3}=s*s*s$ . In other words what number multiplied three times gives 512? Take the cube root of 512 to get $\mathbf{8\hspace{1mm} meters}$ .

8

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

$3\sqrt3$

$2\sqrt3$

$9\sqrt3$

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{162}{6}}$

Simplify.

$\text{side length}=\sqrt{27}$

Reduce.

$\text{side length}=3\sqrt3$

9

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

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{384}{6}}$

Simplify.

$\text{side length}=\sqrt{64}$

Reduce.

$\text{side length}=8$

10

If the surface area of a cube is , find the length of one side of the cube.

Explanation

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{486}{6}}$

Simplify.

$\text{side length}=\sqrt{81}$

Reduce.

$\text{side length}=9$

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