Hello, mathlete!

A trick question! . . . We are told that the volume isA 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?constant.

Therefore: .

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: .

Therefore: .