Precalculus Math Problem/Physics?

Question

A rock dropped into still water sends out concentric ripples. If the radius of the outer ripple increases at the rate of 2ft/s, how fast is the area of the disturbed surface increasing when it is 6 ft in diameter?

The answer is 12pi ft/s^2. Can anyone show me how to get this answer? Help will be appreciated.

Answer 1

The area of the circle is given by A(r) = πr^2. The rate of change of A wlth respect to r is dA/dr = 2πr. With respect to t, dA/dt = dA/dr * dr/dt. dr/dt = 2, so dA/dt = 2πdr/dt = 4πr. When diameter = 6, r = 3. The result is then 12π