Question

how to show relation between volume of cone and cylinder of equal height and radii​

Answer 1

Answer:

Question : What is the ratio of the volume of a cylinder and a cone if the radii of a cylinder and cone of the same height are in the ratio 3:4?

Volume of a cylinder of radius r and height h is

Vcyl = πr2h(1)

Volume of a cone of radius r and height h is

Vcone = 13πr2h(2)

For a cylinder and cone of same height, say h , the ratio of radii is 3 : 4. Let the radius of cylinder be 3r . Then, the radius of cone is 4r . Hence

VcylVcone = π(3r)2h13π(4r)2h= 9r21316r2= 2716

Hence, the ratio is 27 : 16.

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