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

Given =  $\frac{dr}{dt} = 0.7 \ cm/s$
To find =   $\frac{dC}{dt}$            , where C is circumference
we know that the circumference of the circle (C) = $2\pi r$
$\frac{dC}{dt} = \frac{dC}{dr}.\frac{dr}{dt}$                              (by chain rule)
$\frac{dC}{dt} = \frac{d2\pi r}{dr}.\frac{dr}{dt} = 2\pi \times 0.7 = 1.4\pi \ cm/s$
Hence,  the rate of increase of its circumference is $1.4\pi \ cm/s$