Question

A cone, A hemisphere and A cylinder stand on equal faces and have same height as the radius of base show that their volumes are in the ratio 1:2:3

Answer 1

cone = 1/3 pi r^2 h = 1/3 pi r^3 (since height and radius equals)
hemisphere = 2/3 pi r^3
cylinder = pi r^2 h = pi r^3
ratio of the volumes are = 1/3 pi r^3 : 2/3 pi r^3 : pi r^3
                                         = 1/3 : 2/3 : 1
                                        = 1:2:3
 hence proved