If the rate of increase of the radius of a circle is 5 ~cm / sec , then the rate of increase of its area, when the radius is 20 ~cm , will be

Correct answer: (C) 200 π. Hints : A=π r^2 (d r)/(d t)=5 dA/dt=2 π r dr/dt=2 π 20(5) =200 π

Q79 / 160 · WBJEE 2009 · Mathematics

If the rate of increase of the radius of a circle is $5 \mathrm{~cm} / \mathrm{sec}$, then the rate of increase of its area, when the radius is $20 \mathrm{~cm}$, will be

A
$10 \pi$
B
$20 \pi$
Correct answer
C
$200 \pi$
D
$400 \pi$

Solution

Hints : $\mathrm{A}=\pi \mathrm{r}^2 \quad \frac{d r}{d t}=5$ $$ \begin{aligned} & \frac{\mathrm{dA}}{\mathrm{dt}}=2 \pi r \frac{\mathrm{dr}}{\mathrm{dt}}=2 \pi 20(5) \\ & =200 \pi \end{aligned} $$

Hence, the correct answer is option: 'C'.

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