[tex]\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\implies V=\cfrac{4\pi }{3}r^3
\\\\\\
\cfrac{dV}{dt}=\cfrac{4\pi }{3}\cdot \stackrel{chain~rule}{3r^2\cdot \cfrac{dr}{dt}}\quad
\begin{cases}
\frac{dr}{dt}=50\\
r=6
\end{cases}\implies \cfrac{dV}{dt}=\cfrac{4\pi }{3}\cdot 3(6)^2\cdot 50\\\\\\ \cfrac{dV}{dt}=\stackrel{\frac{cm^3}{s}}{7200\pi}[/tex]
