$\begin{array}{1 1}(A)\;60\pi cm^2/s \\ (B)\;30\pi cm^2/s \\(C)\;20\pi cm^2/s \\(D)\;40\pi cm^2/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}$$=3cm/s$

Radius =$10cm.$

Area of the circle =$\pi r^2$

$A=\pi r^2$

Differentiating on both sides w.r.t $t$

$\large\frac{dA}{dt}$$=2\pi r\large\frac{dr}{dt}$

Step 2:

Substituting the values for $r$ and $\large\frac{dr}{dt}$ we get,

$\large\frac{dA}{dt}=$$2\times \pi\times 10\times 3$

$\quad\quad=60\pi cm^2/s$

Hence the rate at which the area of the circle is increasing is $60\pi cm^2/s$

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