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.

Answer 1

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