Question in Calculus

Question

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.1 ft/s.

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

The area is increasing at ?

(b) How rapidly is the area enclosed by the ripple increasing at the end of 7 seconds?

The area is increasing at ?

Answer 1

Area A = πr²;

(a) dA/dt = 2πrdr/dt = 2π·3.1 ft/s·4ft = 77.91 ft²/s.

(b)At the end of 7 s r = 3.1ft/s·7s = 21.7 ft

dA/dt = 2π·3.1ft/s·21.7ft = 422.67 ft²/s