When the linear
dimensions of a three-dimensional shape are all changed by a scale
factor k (i.e multiplied by k ), its volume is changed by a scale
factor of k3 (i.e multiplied by k3).

For example,

the effect of doubling
or trebling the edges of a cube is to increase its volume by factors
2^{3} = 8 or 3^{3} = 27.