Question

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 7 ft/s. How rapidly is the area enclosed by the ripple increasing when the radius is 1 feet?

Answer 1

Explanation:

Let the area of the circular ripple = πr²

r is the radius

Rate at which the area is increasing is;

dA/dt = dA/dr • dr/dt

dA/dr = 2πr

dA/dt = 2πr • dr/dt

Given

dr/dt = 7ft/s

r = 1ft

Substitute

dA/dt = 2π(1)•7

dA/dt = 14π ft²/s

Hence the area is rapidly increasing at 14ft²/s