Question

The radius of a circular oil slick on the surface of a pond is increasing at the rate of 10 meters/min. At what rate is the circle's area changing when the radius of the oil slick is 20 m. ?

Answer 1

Given

$\frac{dr}{dt}=10 m/min$

We have to find $\frac{dA}{dt}$ at r=20 metrs

Now $A=πr^2$

$\frac{dA}{dt}=2πr\frac{dr}{dt}$

At r=20m

$\frac{dA}{dt}=2π \times 20 \times 10=400π \\ \frac{dA}{dt}=1256$

Answer 1256 m/min