How to find the length of an edge of a cube

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

Questions 1 - 10

1

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $27\ m^3$ .

$3\ m$

$6\ m$

$9\ m$

$12\ m$

$15\ m$

Explanation

The formula for the volume of a cube is

,

where is the length of the edge of a cube.

Plugging in our values, we get:

$27\ m^3 = (e)^3$

$e = 3\ m$

2

Our backyard pool holds 10,000 gallons. Its average depth is 4 feet deep and it is 10 feet long. If there are 7.48 gallons in a cubic foot, how wide is the pool?

33 ft

30 ft

7.48 ft

100 ft

133 ft

Explanation

There are 7.48 gallons in cubic foot. Set up a ratio:

1 ft3 / 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft3/ 7.48 gallons) = 1336.9 ft3

Pool Volume = 4ft x 10 ft x WIDTH = 1336.9 cubic feet

Solve for WIDTH:

4 ft x 10 ft x WIDTH = 1336.9 cubic feet

WIDTH = 1336.9 / (4 x 10) = 33.4 ft

3

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.

$\text{side length}=4$

4

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.

$\text{side length}=12$

5

What is the length of an edge of a cube that has a surface area of 54?

Explanation

The surface area of a cube can be determined using the following equation:

$SA=6\times l^2$

$\frac{54}{6}=\frac{6l^2}{6}$

$\sqrt9=\sqrt{l^2}$

6

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.

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

7

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.

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

8

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.

9

Find the length of an edge of the following cube:

Length_of_edge

The volume of the cube is $64\ m^3$ .

$4\ m$

$3\ m$

$6\ m$

$8\ m$

$5\ m$

Explanation

The formula for the volume of a cube is

,

where is the length of the edge of a cube.

Plugging in our values, we get:

$64\ m^3=(e)^3$

$e=4\ m$

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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