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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
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Find the rate of change of the area of a circle with respect to its radius r when $(b)\; r = 4 cm$

This is (b) part of the multi-part question q1

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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 =$\pi r^2\;cm^2$
Radius of the circle =4cm.
$A=\pi r^2$
Differentiating w.r.t $r$ we get,
$\large\frac{dA}{dr}$$=2\pi r$
Substituting for $r$ we get,
$\qquad=2\times \pi\times 4$
$\qquad=8\pi\;cm^2/cm$
answered Jul 5, 2013 by sreemathi.v
edited Jul 5, 2013 by sreemathi.v
 

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