A trick question! . . . We are told that the volume is constant.A potter forms a piece of clay into a cylinder.
As he rolls it, the length, , of the cylinder increases and the radius, , decreases.
Assume that no clay is lost in the process.
Suppose the length of the cylinder is increasing by 0.2 cm/sec.
(a) What is the rate at which the volume is changing?
The volume of a cylinder is: .(b) What is the rate at which the radius is changing
when the radius is 3 cm and the length is 5 cm?
Since the volume is constant, we have: .
Differentiate with respect to time (Product Rule):
We are given: .