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`

Height of cylinder`=h`
Height of Hemisphere `r=h`(r is the radius of sphere)
Volume of cone `V=1/3pir^2h`....(1)
Volume of hemisphere `=2/3pir^2xxr`
`=2/3pixxr^2xxh`
`=2/3pir^2h`....(2)
volume of cylinder `=pir^2h`.....(3)
from equation `1,2 and 3`
`1/3pir^2h:2/3pixxr^2xxh:pir^2h`
`=>1/3:2/3:1`
`1:2:3`