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Question
A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
Solution
Let the diameter of the base for all three be x cm and height be y cm.
For hemisphere radius `x /2 cm`
Height `y = x/2 cm`
(As height of the hemisphere is equal to the radius of hemisphere)
For cone
Radius `= x /2 cm`
Height `= x /2 cm`
(As height is same for all)
For cylinder
Radius `= x /2 cm`
Height `= x /2 cm`
The ratio of their volume is
= cylinder volume : conic volume : hemispherical volume
` = pi (x/2)^2 x /2 :1/3 pi (x/2)^2 (x/2) :2/3 pi (x/3)^3`
`=1 :1/3 :2/3`
`=3:1:2`
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