A stone is dropped into a pool of still water. The waves created move away at a speed of 1.5 ft/sec. How fast is the area of disturbed water increasing 8 s after the stone hits the water?

Answer 1

dr/dt = 1.5

A = πr²

dA/dt = 2πr·dr/dt and at t = 8, r = 8·1.5 = 12 so

dA/dt = 36π ft² / sec