[tex]\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\qquad h=4r\implies V=\cfrac{\pi r^2 \cdot 4r}{3}\implies V=\cfrac{4\pi r^3}{3}\\\\
-----------------------------\\\\
\cfrac{dv}{dt}=\cfrac{4\pi }{3}\cdot 3r^2\cdot \cfrac{dr}{dt}\implies \cfrac{dv}{dt}=4\pi r^2\cdot \cfrac{dr}{dt}\qquad
\begin{cases}
\frac{dr}{dt}=4\\\\
r=7
\end{cases}
\\\\\\
\cfrac{dv}{dt}=4\pi (7)^2\cdot 4[/tex]
