Question

If the volume of a cube is increased by a factor of 8 ,what is the change in the length of the sides of the cube?

Answer 1

The side length of the cube will only go up by a factor of 2.

Think about it like finding the volume of a cube in reverse:


`volume = side^3 = side * side * side`

If we multiply the left and right sides of this equation by 8:


`8 * volume = 8 * (side*side*side)`

And try to "distribute" the 8 by splitting it up into three 2's:


`8*volume = 2*2*2*(side*side*side)`

`8*volume = 2*side * 2*side * 2*side`
`8*volume = (2*side) * (2*side) * (2*side)`
`8*volume = (2*side)^3`

We can see the side length only doubles.