Consider everything a function of time (t). For your circle:

suggests

We find the derivative with respect to t = time.

On the left-had side, we have simply

.

On the right-hand side, we have

Putting it all together (and dispensing with the cumbersome '(t)' notation), we get

Knowing this, one is armed with enough to solve many problem types.

Actually, we may also want to dispose of the cumbersome 'dt' notation and just go with the differential usage.

In words, this says, "The change in the area is

multiplied by the change in the radius.

We are given dr = 15 cm/s.

Let's see what you get.