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 - 6

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

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:

$SA=6\times l^2$

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

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

4

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:

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

$e=4\ m$

5

Given that the suface area of a cube is 72, find the length of one of its sides.

$2\sqrt{3}$

$3\sqrt{2}$

$\sqrt{6}$

Explanation

The standard equation for surface area is

where denotes side length. Rearrange the equation in terms of to find the length of a side with the given surface area:

$a=\sqrt{\frac{SA}{6}}=\sqrt{\frac{72}{6}}=\sqrt{12}=2\sqrt{3}$

6

A cube has a volume of 64cm3. What is the area of one side of the cube?

16cm2

4cm

4cm2

16cm3

16cm

Explanation

The cube has a volume of 64cm3, making the length of one edge 4cm (4 * 4 * 4 = 64).

So the area of one side is 4 * 4 = 16cm2

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