UPSC NDA Math Model Paper 2

Let's say that the radius of the circle is r meters and let t be the time in seconds.
It is given that

dr

dt

=−

2

π

m∕sec.
Now, Area of the circle: A=πr2m2
Using the chain rule of derivatives:

dA

dt

=

dA

dr

×

dr

dt

⇒

dA

dt

=2πr×

−2

π

m2∕sec
⇒

dA

dt

=−4rm2∕sec
When the radius is 10 m, the rate of change of area will be: -40 m2∕sec
NOTE: A negative value of the rate of change indicates a decrease