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Question

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.
 


Solution

Bases and heights of a cones hemisphere and a cylinder are equal
Let r be the radius and h be their heights
now volume of cone =13πr2h
Volume of Hemisphere =23πr3
 and volume of cylinder =πr2h
  Ratio in thir volumes
=13πr2h:23πr3:πr2h=13h:23r:h=13h:23h:h=13:23:1=1:2:3
 

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