Question

If the surface area of a cube is 96 square inches, what is the volume of the cube?

Answer 1

See a solution process below:

Explanation:

A cube is made up of 6 squares.

So if the surface area of the cube is `96"in"^2` the the area of one square is:

`(96"in"^2)/6 = 16"in"^2`

The area of a square is determined by the formula:

`A = s^2` Where `s` is the length of the side of the square.

We can substitute the value above for the area of the square and solve for `s` giving:

`16"in"^2 = s^2`

`sqrt(16"in"^2) = sqrt(s^2)`

`4"in" = s`

`s = 4"in"`

The formula for the volume of a cube is:

`V = s^3` Where `s` is the length of the side of the cube.

Substituting for `s` with the value we calculated above and calculating `V` gives:

`V = (4"in")^3`

`V = 64"in"^3`

The volume of a cube with surface area 96 inches squared is 64 cubic inches.

Answer 2

`V="64 in"^3"`

Refer to the explanation for the process.

Explanation:

You need to find the length on one side of the cube, and then cube the side to get volume.

The surface area of a cube is equal to `6a^2`, where `a` is the length of a side. So divide `"96 in"^2"` by `6`. This will give you the surface area of one side of the cube.

`SA=("96 in"^2)/6="16 in"^2"`

The length, `a` of a side of a cube is the square root of the surface area of one side.

`L=sqrt16`

`L=4`

The volume of a cube is `a^3`.

`V=4^3`

`V="64 in"^3"`