## Example Questions

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### Example Question #1 : How To Find The Volume Of A Cube

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

26

18

20

24

None of the answers are correct

26

Explanation:

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

4.18x3

5.28x3

6.73x3

3.82x3

8.00x3

3.82x3

Explanation:

Vcube = s3 = (2x)3 = 8x3

Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x

### 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?      Explanation:

Weight = Density * Volume

Volume of Gold Cube = side3= x3

Weight of Gold = 16 g/cm3 * x3

Weight of Glass = 3/cm3  * side3

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

16* x3 = 2  * side3

side3 = 16/2* x3 =  8 x3

Take the cube root of both sides:

side = 2x

### Example Question #2 : How To Find The Volume Of A Cube

Chemicals to clean a swimming pool cost \$0.24 per cubic foot of water. If a pool is 6 feet deep, 14 feet long and 8 feet wide, how much does it cost to clean the pool? Round to the nearest dollar.      Explanation:

The volume of the pool can be determined by multiplying the length, width, and height together. Each cubit foot costs 24 cents, so: ### Example Question #1 : How To Find The Volume Of A Cube

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?      Explanation:

If we let represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of is 27 times as large as the small cube's volume of .

### Example Question #1 : How To Find The Volume Of A Cube

A tank measuring 3in wide by 5in deep is 10in tall.  If there are two cubes with 2in sides in the tank, how much water is needed to fill it?      Explanation:       ### Example Question #3 : How To Find The Volume Of A Cube

What is the volume of a cube that has a side length of inches?      Explanation:

We are given the side length of a cube so we simply plug that into the formula for the volume of a cube.

That formula is , and so the correct answer is .

Make sure to check your units, is the correct number, but the units are squared rather than cubed.

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

What is the volume of a cube with a side of length 1 cm?      Explanation:

The formula for the volume of a cube with a side of length is: ### Example Question #5 : How To Find The Volume Of A Cube

A cube of sponge has volume . When water is added, the sponge triples in length along each dimension. What is the new volume of the cube, in cubic centimeters?      Explanation:

If our original cube has a volume of , then the length of one of its edges is . Triple each edge to , then cube the result, and we obtain ### Example Question #6 : How To Find The Volume Of A Cube

Find the volume of a cube with side length 10.       