Question

The volume of a cube, in cubic centimeters, is given by the function V(x) = x³. Write a new function for the volume of the cube with cubic millimeters as the units.

Answer 1

We have the following:

let x, centimeters

now,

we look for the equivalence between centimeters and millimeters

1 centimeter = 10 milimeters

x centimeters = 10x milimeters

$\begin{gathered} v(x)=(10x)^3 \\ v(x)=10^3x^3=1000x^3 \end{gathered}$

The new function for volume of the cube with cubic milimeters as units is:

$v(x)=1000\cdot x^3$