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Question
Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
Solution
Let the radius of the sphere be r.
We have,
The radius of the cone = The radius of the cylinder = The radius of the sphere = r and
The height of the cylinder = The height of the cone = The height of the sphere = 2r
Now,
Volume of the cylinder `= pi"r"^2(2"r") = 2pi"r"^3`
Volume of the cone `= 1/3 pi"r"^2 (2"r") = 2/3 pi"r"^3` and
Volume of the sphere`=4/3pi"r"^3`
So,
The ratio of the Volumes of the cylinder, the cone and the sphere `= 2pi"r"^3 : 2/3pi"r"^3 : 4/3pi"r"^3`
`= 1 : 1/3 : 2/3`
`= 3 : 1 : 2`
So, the ratio of the volumes of the cylinder, the cone and the sphere is 3 : 1 : 2.
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