[tex]\bf \textit{volume of a cylinder}\\\\
V=\pi r^2h~~
\begin{cases}
r=x\\
h=y
\end{cases}\implies V=x^2y\pi
\\\\\\
\textit{volume of a cone}\\\\
V=\cfrac{\pi r^2h}{3}\qquad r=2x\implies V=\cfrac{\pi (2x)^2 h }{3}
\\\\\\
\textit{and since both volumes are equal, then}
\\\\\\
\stackrel{cylinder's}{x^2y\pi }~~~~=~~~~\stackrel{cone's}{\cfrac{\pi (2x)^2h}{3}}[/tex]
[tex]\bf x^2y\pi =\cfrac{\pi (2^2x^2)h}{3}\implies x^2y\pi =\cfrac{4x^2h\pi }{3}\implies \cfrac{x^2y\pi }{4x^2\pi }=\cfrac{h}{3}
\\\\\\
\cfrac{y}{4}=\cfrac{h}{3}\implies \cfrac{3y}{4}=h[/tex]
