UPSC NDA Math Model Paper 3

The area of a circle A with radius r is given by A=πr2
∴ The rate of change of area (A) with respect to time (t) is given by chain rule is −

dA

dt

=

d(πr2)

dt

=

d(πr2)

dt

.

dr

dt

=2πr.

dr

dt

It is given that :

dr

dt

=5cm
∴

dA

dt

=2π(8)(5)=80π
So when the radius of the circular wave will be 8 cm, the enclosed area will increase at the rate of 80π cm2s−1