A stone is dropped into a quiet lake and waves move in circles at speed of $8 \mathrm{~cm} / \mathrm{sec}$. At the instant when the radius of the circular wave is 12 cm . how fast is the enclosed area increasing?

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Aicharya · Accepted Answer

Given, the rate of increasing the radius $\begin{aligned} & =\frac{\mathrm{dr}}{\mathrm{dt}}=8 \mathrm{~cm} / \mathrm{sec} \ & 	ext { Area }=A=\pi r^2 \ & 	herefore \quad \frac{\mathrm{dA}}{\mathrm{dt}}=2 \pi \mathrm{dr} \ & \Rightarrow \frac{\mathrm{dA}}{\mathrm{dt}}=2 \pi(12)(8) \ & \ldots[\because \mathrm{r}=12 \mathrm{~cm}] \ & =192 \pi \mathrm{~cm}^2 / \mathrm{sec} \end{aligned}$

A stone is dropped into a quiet lake and waves move in circles at speed of $8 \mathrm{~cm} / \mathrm{sec}$.…

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