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Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is

$(A)\; 10\pi \qquad (B) \;12\pi \qquad (C)\; 8\pi \qquad (D)\; 11\pi$

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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 $x=x_0$
Area of the circle $A=\pi r^2$
Differentiating w.r.t $r$ we get,
$\large\frac{dA}{dr}$$=2\pi r \large\frac{dA}{dr}_{(r=6)}$$=2\pi\times 6$
$\Rightarrow 12\pi$
Hence $B$ is the correct option.
answered Jul 8, 2013

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