Question

We have two cubes. If the edge of the larger cube is two times the length of the smaller cube, how many times greater is the volume of the larger cube compared to the smaller cube?

Answer 1

See a solution process below:

Explanation:

The formula for the volume of a cube is:

`V_c = s^3`

Where `s` is the length of one edge or side of the cube.

The Volume of the larger cube we will call `V_l` is:

`V_l = (2x)^3`

`V_l = 2^3x^3`

`V_l = 8x^3`

The Volume of the smaller cube we will call `V_s` is:

`V_s = x^3`

If we divide the `V_l` by `V_s` we get:

`V_l/V_s => (8x^3)/x^3 => (8color(red)(cancel(color(black)(x^3))))/color(red)(cancel(color(black)(x^3))) => 8`

The volume of the larger cube is 8 times greater than the volume of the smaller cube.

Answer 2

c) 8 times bigger ... maybe.

Explanation:

If you mean the sides are 2x in length and x in length for the large and small cubes respectively, then the larger is 8 times greater in volume.

Volume of a cube = `l^3` where `l` is the length of each side.

I hope this helps,
Steve

Answer 3

Correct answer is c) 8

Explanation:

The volume of a cube that has sides equal to `x` is `x^3`.

So, if we double the length of every side (making it `2x`), the volume becomes `(2x)^3` = `2^3 xx x^3 = 8x^3`