How fast is the volume of a cylinder changing with respect to the radius when the radius is mm and the height is a constant 5mm?
The change will be proportional to the square of the radius.
Given two cylinders with the same height and radii r1 and r2 their volume will be:
The ratio of volumes between them will be:
This means that these two cylinders are correlated by the square of radius.
The general formula for the volume of a cylinder is
We are told that the height is constant, so this cylinder has volume
The rate of change of volume with respect to radius is
The volume is changing at a rate of