The volume of a cylinder is given by
[tex]V=\pi hr^2[/tex]
Whereas the volume of a cone is given by
[tex]V=\dfrac{1}{3}\pi hr^2[/tex]
Since the cylinder has radius x and height y, its volume is
[tex]V = \pi x^2y[/tex]
And since the cone has a radius 2x, its volume is
[tex]V = \pi (2x)^2 h = 4\pi x^2h[/tex]
where h is the height of the cone.
We know that the two volumes are the same, so we can build the equation and solve it for h:
[tex]\pi x^2y = 4\pi x^2h[/tex]
Simplify [tex]\pi x^2[/tex] from both sides:
[tex]y = 4h[/tex]
Divide both sides by 4:
[tex]h = \dfrac{y}{4}[/tex]
