### All High School Math Resources

## 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:**

133 ft

30 ft

7.48 ft

100 ft

33 ft

**Correct answer:**

33 ft

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

1 ft^{3} / 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft^{3}/ 7.48 gallons) = 1336.9 ft^{3}

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

### Example Question #1 : How To Find The Length Of An Edge Of A Cube

A cube has a volume of 64cm^{3}. What is the area of one side of the cube?

**Possible Answers:**

4cm

16cm

4cm^{2}

16cm^{2}

16cm^{3}

**Correct answer:**

16cm^{2}

The cube has a volume of 64cm^{3}, making the length of one edge 4cm (4 * 4 * 4 = 64).

So the area of one side is 4 * 4 = 16cm^{2}

### Example Question #1 : Cubes

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

**Possible Answers:**

**Correct answer:**

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:

### Example Question #2 : Cubes

Find the length of an edge of the following cube:

The volume of the cube is .

**Possible Answers:**

**Correct answer:**

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:

### Example Question #1 : How To Find The Length Of An Edge Of A Cube

Find the length of an edge of the following cube:

The volume of the cube is .

**Possible Answers:**

**Correct answer:**

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:

### Example Question #4 : Cubes

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

**Possible Answers:**

**Correct answer:**

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