A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.
Volume of a hemisphere = (2/3)πr3
Volume of a right circular cone = (1/3)πr2h
Volume of a cylinder = πr2h
Given, a cone, a hemisphere and a cylinder stand on equal bases and have the same height.
Height of a hemisphere is the radius and equal bases implies equal base radius.
Thus, height of cone = height of cylinder = base radius = r
Ratio of volumes = (1/3)πr2h : (2/3)πr3 : πr2h
⇒ Ratio of volumes = r3 : 2r3 : 3r3 = 1 : 2 : 3