The side length of a cube is quadrupled. write a ratio to compare the volume of the original cube to the volume of the new cube.

The answer is 1:64

Let's say that the original cube had side lengths of 1 unit. The volume would be 1*1*1 = 1 cubic unit.

If we quadruple each side, then the new cube has side lengths of 4. The new volume is 4*4*4 = 64

The old volume (1 cubic unit) pairs up with the new volume (64 cubic units) to form the ratio 1:64

Side notes:
* The order is important. We cannot say 64:1 because the old volume is mentioned first

* We can write the equation y = 64*x where x is the old volume and y is the new volume.