Question

Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Answer 1

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.