When a rock is thrown into a calm pond, circular waves, which have the same centre, are created. Find the rate of change of the growing surface area which is enclosed by the outermost wave at time 4 seconds, given that its radius grows at 1 m/sec.
At t seconds, let r be the radius, and let S be the surface are enclosed by the outermost wave.

The area of a circle is

Differentiate wrt time.



We are given that dr/dt=1

If the radius increases 1 meter per second, then after 4 seconds it is 4 meters.

Plug in your knowns and you're all set.