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

At any instant of time t let the radius of the circle be r and its circumference be C, then $C=2\pi r$
Rate of increase of circumference $\frac{dC}{dt}=2\pi \frac{dr}{dt}$
(Differentiating w.r.t. t, by chain rule)
Where, \frac{dr}{dt} is rate of increase of radius, so $\frac{dr}{dt}=0.7cm/s$
$\therefore \frac{dC}{dt}=2\pi \left(0.7\right)cm/s=1.4\pi cm/s(\because \frac{dr}{dt}=0.7cm/sgiven)$
Hence, rate of increase of circumference is $1.4\pi cm/s$