A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.4 ft/s.

Question

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.4 ft/s.

(a) How rapidly is the area enclosed by the ripple increasing when the radius is 4 feet?

The area is increasing at

ft^2/s.

(b) How rapidly is the area enclosed by the ripple increasing at the end of 7.8 seconds?

The area is increasing at

ft^2/s.

Answer 1

dr/dt = + 2.4

A = πr². Differentiating w respect to t gives

dA/dt = 2πr·dr/dt

Plug in r = 4 and the value for dr/dt for part a).

For part b, we need a value for r but we know it increases at a constant rate of 2.4 ft / sec for 7.8 secs so we will leave it as an exercise for the reader to determine the value of r.