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.