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

$\begin{array}{1 1} 1.2\pi \;cm/s \\ 1.4\pi \;cm/s \\ 1.4m/s \\ 14cm/s \end{array}$

Toolbox:
• If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
• $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$
Step 1:
Given : $\large\frac{dr}{dt}$$=0.7cm/s Circumference of the circle is 2\pi r c=2\pi r Differentiating w.r.t t on both sides, \large\frac{dc}{dt}$$=2\pi \large\frac{dr}{dt}$
Step 2:
Substituting the value for $\large\frac{dr}{dt}$ we get,
$\large\frac{dc}{dt}$$=2\pi\times 0.7$
$\quad=1.4cm/s$
Hence the rate of increase in the circumference is $1.4cm/s$