Given a cube with edges expanding at a rate of 1 centimeter per second, what is the rate of change of the volume of the cube when the length of an edge is:

- 5cm.
- 10cm.
- cm.

First, we know the volume of a cube is given by

where is the length of an edge. Thus, the rate of change of the volume relative to the rate of change of an edge is given by

We use this formula to find the rate of change of the volume for given values of ,

- If then we have
- If then we have
- If then we have

If the rate of change in the volume of a cube equal to the rate of change in its side then the length of side is