Question

What happens to the volume of a cube if the length of an edge is doubled?

Answer 1

Doubled: Volume increased 8 times
Tripled: Volume increased 27 times
Quadrupled: Volume increased 64 times

Pretty simple... if you're doubling the lengths, you're increasing them by 2 times. Take 2 and raise it to the 3rd power. If you're tripling the lengths, you're increasing them 3 times over. Take 3 and raise it to the 3rd power. And so on.

Doubled = 2^3 = 8
Tripled = 3^3 = 27
Quadrupled = 4^3 = 64

Does that make sense?

Answer 2

The new volume of the larger cube becomes eight times of the smaller cube.

Explanation:

Let the edge of the cube be x.

Volume of cube = V =
`x^3`..[1]

If we double the edge of the cube, then edge of the cube becomes = 2x

The volume of cube whose edges are doubled = V'

`V'=(2x)^3=8x^3`,..[2]

Dividing [1] and [2]:

`(V)/(V')=(x^3)/(8x^3)`

`V'=8* V`

The new volume of the larger cube becomes eight times of the smaller cube.