Vol of cylinder = $π$r$^2$H = vol of cone = $\;{1}/{3}$$π$r$^2$h
H = height of cylinder and h = height of cone
Let y = radius of cylinder = y, then radius of cone = 2y
$π$y$^2$H = $\;{1}/{3}$$π$(2y)$^2$h
y$^2$H = $\;{1}/{3}$4y$^2$h ( $π$ cancels out and cross multiplying)
The ratio of the height of the cylinder to that of the cone = $\;{\;\text "H"\;}/{\;\text "h"\;}$ = $\;{4y^2}/{3y^2}$
= $\;{4}/{3}$ = 4: 3 (y$^2$ cancels out )
