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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
Let r be the radius of the base.
and h be the height.
Here, h = r.
Now,
The ratio of their volumes will be
Volume of cone : volume of hemisphere : volume of a cylinder
`1/3pir^2 h : 2/3 pir^3 : pir^2h`
`V_1 : V_2 :V_3 = 1/3pir^3 :2/3 pir^3 :pir^3 `
Hence `V_1 :V_2 :V_3 = 1:2:3`
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