ACT Math - How to find the volume of a cube

Find the volume of a cube with side length 10.

$10\sqrt{2}$

Explanation

To find volume, simply cube the side length. Thus,

Find the volume of a cube given side length is .

Explanation

To solve, simply cube the side length. Thus,

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.

$V = 6 \times 8 \times 14 = 672 ft^{3}$

Each cubit foot costs 24 cents, so:

$672ft^3\times $0.24=$161.28\approx $161$

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 $\sqrt[3]{1000} = 10cm$ . Triple each edge to , then cube the result, and we obtain

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

3.82x3

8.00x3

5.28x3

4.18x3

6.73x3

Explanation

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

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

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 $x^{3}$ .

The larger cube has edges three times as long, so the length can be represented as . The volume is $(3x)^{3}$ , which is $27x^{3}$ .

The large cube's volume of $27x^{3}$ is 27 times as large as the small cube's volume of $x^{3}$ .

The density of gold is $16\ g/cm^3$ and the density of glass is $2\ g/cm^3$ . You have a gold cube that is $x\ cm$ 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

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.

Find the volume of a cube whose side length is 0.1.

Explanation

To solve, simply use the formula for volume of a cube. The volume of a cube is length times width times height. Since the height, width, and length are equal on a cube the formula becomes side cubed.

We are given the side length of 0.1 thus,