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Question
A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.
Solution
Let r be the common radius thus,
h = height of the cone = height of the cylinder = 2r
Let
`V_1= Volume of sphere = 4/3 πr^3`
`V_2= "Volume of cylinder" = π r^2 xx2r =2πr^3`
`V
_3= Volume of the cone =1/3π r^2 xx 2r=2/3πr^3`
Now ,
`V_1:V_2:V_3= 4/3πr^3 : 2π r^3`
=4:6:2
=2:3:1
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