The radius of a circle is increasing at the rate of 0.7 cm/s.

The circumference of a circle (C) with radius (r) is given by

$C=2 \pi r .$

Therefore, the rate of change of circumference (C) with respect to time (t) is given by,

$\frac{d C}{d t}=\frac{d C}{d r} \cdot \frac{d r}{d t}$ (By chain rule)

$=\frac{d}{d r}(2 \pi r) \frac{d r}{d t}$

$=2 \pi \cdot \frac{d r}{d t}$

It is given that $\frac{d r}{d t}=0.7 \mathrm{~cm} / \mathrm{s}$.

Hence, the rate of increase of the circumference is $2 \pi(0.7)=1.4 \pi \mathrm{cm} / \mathrm{s}$.