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

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Example Questions

Example Question #1 : Cubes

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?

Possible Answers:

100 ft

30 ft

33 ft

133 ft

7.48 ft

Correct answer:

33 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

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Example Question #1 : Cubes

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

Possible Answers:

16cm

4cm²

16cm²

4cm

16cm³

Correct answer:

16cm²

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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Example Question #2 : How To Find The Length Of An Edge Of A Cube

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

Possible Answers:

$\sqrt{6}$ $\displaystyle \sqrt{6}$

$2\sqrt{3}$ $\displaystyle 2\sqrt{3}$

$\displaystyle 3$

$\displaystyle 6$

$3\sqrt{2}$ $\displaystyle 3\sqrt{2}$

Correct answer:

$2\sqrt{3}$ $\displaystyle 2\sqrt{3}$

Explanation:

The standard equation for surface area is

SA=6a^2 $\displaystyle SA=6a^2$

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

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

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Example Question #1 : Cubes

Find the length of an edge of the following cube:

Length_of_edge

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

Possible Answers:

$3\ m$ $\displaystyle 3\ m$

$9\ m$ $\displaystyle 9\ m$

$12\ m$ $\displaystyle 12\ m$

$6\ m$ $\displaystyle 6\ m$

$15\ m$ $\displaystyle 15\ m$

Correct answer:

$3\ m$ $\displaystyle 3\ m$

Explanation:

The formula for the volume of a cube is

V=(e)^3 $\displaystyle V=(e)^3$,

where $\displaystyle e$ is the length of the edge of a cube.

Plugging in our values, we get:

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

$e = 3\ m$ $\displaystyle e = 3\ m$

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Example Question #1 : Cubes

Find the length of an edge of the following cube:

Length_of_edge

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

Possible Answers:

$8\ m$ $\displaystyle 8\ m$

$6\ m$ $\displaystyle 6\ m$

$3\ m$ $\displaystyle 3\ m$

$4\ m$ $\displaystyle 4\ m$

$5\ m$ $\displaystyle 5\ m$

Correct answer:

$4\ m$ $\displaystyle 4\ m$

Explanation:

The formula for the volume of a cube is

V=(e)^3 $\displaystyle V=(e)^3$,

where $\displaystyle e$ is the length of the edge of a cube.

Plugging in our values, we get:

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

$e=4\ m$ $\displaystyle e=4\ m$

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Example Question #1881 : High School Math

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

Possible Answers:

$\displaystyle 6$

$\displaystyle 9$

$\displaystyle 3$

$\displaystyle 12$

Correct answer:

$\displaystyle 3$

Explanation:

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

$SA=6\times l^2$ $\displaystyle SA=6\times l^2$

54=6l^2 $\displaystyle 54=6l^2$

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

9=l^2 $\displaystyle 9=l^2$

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

3=l $\displaystyle 3=l$

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

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Cubes

Example Question #1 : Cubes

Example Question #2 : How To Find The Length Of An Edge Of A Cube

Example Question #1 : Cubes

Example Question #1 : Cubes

Example Question #1881 : High School Math

All High School Math Resources

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