### All ACT 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:**

33 ft

100 ft

30 ft

7.48 ft

133 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:**

16cm^{2}

4cm^{2}

16cm^{3}

16cm

4cm

**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 #11 : Solid Geometry

A cube as the volume of .

Find the length of a side of this cube.

**Possible Answers:**

**Correct answer:**

The formula to find the volume of the cube is

Since we know the volume, we can set up the equation

### Example Question #2 : Cubes

A cube has a surface area of , what is the length of the side of the cube? (If necessary, round to the nearest hundredth.)

**Possible Answers:**

**Correct answer:**

To find the length of the side of a square given the surface area, use the surface area formula and solve for :

, now divide both sides by 6

, now square root both sides

.

### Example Question #3 : Cubes

A certain cubic box when unfolded and laid flat on a table covers exactly square units of space. What is the width of the box, in units?

**Possible Answers:**

**Correct answer:**

To find the length of the edge of a cube from its surface area, remember that , where is the length of a side.

So, the box is units long.

### Example Question #21 : Solid Geometry

Given the volume of a cube is , find the side length.

**Possible Answers:**

**Correct answer:**

To find side length, simply realize that volume is the side length cubed. Thus,

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

Find the length of the edge of a cube given the volume is .

**Possible Answers:**

**Correct answer:**

To solve, simply take the cube root of the volume. Thus,