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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} $

1 Answer

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 $1.4cm/s$
answered Jul 5, 2013 by sreemathi.v
 

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