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

Let at any instant of time $t$, the radius of the circle be $r$ and its circumference be $C$, then $C = 2\pi r$ …(i)

Differentiating (i) w.r.t. $t$, we get
$\cfrac{{dC}}{{dt}} = 2\pi \cfrac{{dr}}{{dt}} = 2\pi (0.7){\rm{cm/sec}}$
$= (1.4\pi ){\rm{cm/sec}}$

Therefore the rate of increase of circumference $= (1.4\pi ){\rm{cm/sec}}$