Question 450765
Let the common volume and radius be equal to V and r, and let the heights of the cone and cylinder be *[tex h_c] and *[tex h_{cyl}] respectively. Using the area for a cone,



*[tex \LARGE V = \frac{1}{3} \pi r^2 h_c]


And for a cylinder,


*[tex \LARGE V = \pi r^2 h_{cyl}]


These two are equal, so


*[tex \LARGE \frac{1}{3} \pi r^2 h_c = \pi r^2 h_{cyl}]


*[tex \LARGE \frac{1}{3} h_c = h_{cyl}]


*[tex \LARGE h_c = 3h_{cyl}]


Hence, the height of the cone is three times as much as the height of the cylinder.