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

62.83185 ft/s

Step-by-step explanation:

r = Radius of circle

t = Time

`(dr)/(dt)` = 2 ft/s

A = Area of circle

`A=\pi r^2`

Differentiating with respect to time

`(dA)/(dt)=2\pi r(dr)/(dt)`

when r = 5 feet

`(dA)/(dt)=2\pi 5* 2\\\Rightarrow (dA)/(dt)=62.83185\ ft/s`

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