Answer:
62.83185 ft/s
Explanation:
r = Radius of circle
t = Time
[tex]\frac{dr}{dt}[/tex] = 2 ft/s
A = Area of circle
[tex]A=\pi r^2[/tex]
Differentiating with respect to time
[tex]\frac{dA}{dt}=2\pi r\frac{dr}{dt}[/tex]
when r = 5 feet
[tex]\frac{dA}{dt}=2\pi 5\times 2\\\Rightarrow \frac{dA}{dt}=62.83185\ ft/s[/tex]
The area is increasing at a rate of 62.83185 ft/s
