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.

Explanation

A cone, a hemisphere, and a cylinder stand on equal bases.
Hence radius of base of cone = radius of hemisphere = radius of cylinder`=r`
They also have same height `=h`
Height of cone` =h`
Hight of cylinder`=h`
Height of Hemisphere `r=h`(r is the radius of sphere)
Volume of cone `=1/3pir^2h`....(1)
Volume of hemisphere`=2/3pir^2xxr=2/3pir^2h`.......(2)
Volume of cylinder`=pir^2h`........(3)
From equation 1,2 and 3,`1/3pir^2h:2/3pir^2h:pir^2h`
`1/3:2/3:1`
`1:2:3`