How much greater is the volume of a cube if the edges are made 10 times longer?

Question

campbell_st · Answer

well if a cube has edge length 1 cm then the volume is 1 cm^3

if its increased to 10cm the volume becomes 1000 cm^3

this is a simple way to look at the change in volume.... 

you can work out the scaling factor... 

see if there is any change in the scaling factor if the edge length is changed 
to 2cm..

directrix · Answer

Suppose that the edge of the cube is x.
Then, the volume is x*x*x = x^3

Now, each side is multiplied by 10 so the edge of the enlarged cube is 10x.
The volume of the new cube is (10x) times (10x) times (10x) = 1000 x^3.

So how many times the original volume of x^3 is the new volume of 1000 x^3?