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

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- 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 $1.4cm/s$

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