Question

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

Answer 1

It is given that the radius of the circle is increasing at a rate of 0.7 cm/s.

Let the radius of circle be r cm.

The formula for the circumference of the circle is,

C=2πr

Differentiate the circumference C with respect to time t,

dC dt = d( 2πr ) dt =2π dr dt

It is given that dr dt =0.7 cm/s. Therefore,

dC dt =2π( 0.7 ) =1.4π cm/s

Thus, the circumference is increasing at a rate of 1.4πcm/s.