A pebble is dropped into a pond, causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate of 2 feet per second. When the radius is 10 feet, at what rate is the total area A of the disturbed water changing?

Answer 1

a = pi r^2
da/dt = 2pi r dr/dt
when r = 10,

da/dt = 2pi * 10 ft * 2 ft/s = 40pi ft^2/s