a spherical balloon is being inflated by pumping in 16cm^3/s of gas.at the instant when balloon contains 36picm^3 of gas.how fast is its radius increasing?

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$$\begin{gathered} \mathrm{Rate} \mathrm{of} \mathrm{change} \mathrm{of} \mathrm{volume} \mathrm{is} \mathrm{given} \mathrm{by} \\ \frac{\mathrm{dV}}{\mathrm{dt}}=16 {\mathrm{cm}}^3/\sec \\ \mathrm{V}=\frac{4}{3}{\mathrm{\pi r}}^3 \\ \mathrm{Differentiate} \mathrm{with} \mathrm{respect} \mathrm{to} \mathrm{time} \\ \frac{\mathrm{dV}}{\mathrm{dt}}=\frac{4}{3}.3{\mathrm{\pi r}}^2.\frac{\mathrm{dr}}{\mathrm{dt}} \\ \frac{\mathrm{dV}}{\mathrm{dt}}=4{\mathrm{\pi r}}^2.\frac{\mathrm{dr}}{\mathrm{dt}} \\ \Rightarrow 16=4{\mathrm{\pi r}}^2.\frac{\mathrm{dr}}{\mathrm{dt}}...\left(\mathrm{i}\right) \\ \mathrm{Now} \\ \mathrm{When} \\ \mathrm{V}=36 \mathrm{\pi } {\mathrm{cm}}^3 \\ \Rightarrow \frac{4}{3}{\mathrm{\pi r}}^3=36 \mathrm{\pi } \\ \Rightarrow {\mathrm{r}}^3=27 \\ \Rightarrow \mathrm{r}=3 \mathrm{cm} \\ \mathrm{Put} \mathrm{in} \left(\mathrm{i}\right) \\ \Rightarrow 16=4\mathrm{\pi }\times 9.\frac{\mathrm{dr}}{\mathrm{dt}} \\ \Rightarrow \frac{\mathrm{dr}}{\mathrm{dt}}=\frac{4}{9\mathrm{\pi }} \mathrm{cm}/\sec \left[\mathrm{Answer}\right] \end{gathered}$$

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