### All ACT Math Resources

## Example Questions

### Example Question #6 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a volume of ? Round your answer to the nearest hundreth if necessary

**Possible Answers:**

**Correct answer:**

First we need to find the side length of the cube. Do that by taking the cube root of the volume.

=

Next plug the side length into the formula for the surface area of a cube:

### Example Question #7 : How To Find The Surface Area Of A Cube

What is the surface area, in square inches, of a cube with sides measuring ?

**Possible Answers:**

**Correct answer:**

The surface area of a cube is a measure of the total area of the** **surface of all of the sides of that cube.

Since a cube contains square sides, the surface area is times the area of a square side.

The area of one square side is sidelength sidelength, or in this case. Therefore, the surface area of this cube is square inches.

### Example Question #8 : How To Find The Surface Area Of A Cube

What is the length of the side of a cube whose surface area is equal to its volume?

**Possible Answers:**

There is not enough information to determine the answer.

**Correct answer:**

To find the side length of a cube whose surface area is the same as its volume, set the surface area and volume equations of a cube equal to each other, the solve for the side length:

Set these two formulas equal to eachother and solve for s.

### Example Question #9 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a side of length ?

**Possible Answers:**

**Correct answer:**

To find the surface area of a cube with a given side length, use the formula:

### Example Question #10 : How To Find The Surface Area Of A Cube

Find the surface area of a cube whose side length is .

**Possible Answers:**

**Correct answer:**

To find surface area of a cube, simply calculate the area of one side and multiply it by . Thus,

### Example Question #11 : How To Find The Surface Area Of A Cube

Find the surface area of a cube whose side length is .

**Possible Answers:**

**Correct answer:**

To find surface aarea, simply multiply the area of a face by 6 since there are 6 faces. Thus,

### Example Question #12 : How To Find The Surface Area Of A Cube

Find the surface area of a cube with side length .

**Possible Answers:**

**Correct answer:**

To solve, simply multiply the face area by . Thus,

### Example Question #4 : How To Find The Volume Of A Cube

What is the sum of the number of vertices, edges, and faces of a cube?

**Possible Answers:**

18

26

None of the answers are correct

24

20

**Correct answer:**

26

Vertices = three planes coming together at a point = 8

Edges = two planes coming together to form a line = 12

Faces = one plane as the surface of the solid = 6

Vertices + Edges + Faces = 8 + 12 + 6 = 26

### Example Question #12 : How To Find The Volume Of A Cube

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

**Possible Answers:**

5.28x^{3 }

8.00x^{3}

4.18x^{3 }

6.73x^{3 }

3.82x^{3}

**Correct answer:**

3.82x^{3}

V_{cube} = s^{3} = (2x)^{3} = 8x^{3}

V_{sphere} = 4/3 πr^{3} = 4/3•3.14•x^{3} = 4.18x^{3 }

### Example Question #13 : How To Find The Volume Of A Cube

The density of gold is and the density of glass is . You have a gold cube that is in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

**Possible Answers:**

**Correct answer:**

Weight = Density * Volume

Volume of Gold Cube = side^{3}= x^{3}

Weight of Gold = 16 g/cm^{3 }* x^{3}

Weight of Glass = 3/cm^{3} * side^{3}

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x^{3} = 2 * side^{3}

side^{3} = 16/2* x^{3 }= 8 x^{3}

Take the cube root of both sides:

side = 2x

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