Question

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2 ft/s. (a) How rapidly is the area enclosed by the ripple increasing when the radius is 5 feet?

Answer 1

Answer:

62.83185 ft/s

Explanation:

r = Radius of circle

t = Time

$\frac{dr}{dt}$ = 2 ft/s

A = Area of circle

$A=\pi r^2$

Differentiating with respect to time

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

when r = 5 feet

$\frac{dA}{dt}=2\pi 5\times 2\\\Rightarrow \frac{dA}{dt}=62.83185\ ft/s$

The area is increasing at a rate of 62.83185 ft/s