Question

The radius and height of a cylinder, a cone and a sphere are same. Calculate the ratio of their volumes. 

Answer 1

Let r, h be the radius and height of Cylinder, Cone and Sphere. 

Volume of cylinder = `pir^2h`

Volume of sphere = `4/3pir^3`      (h = 2r  for sphere)

Volume of cone = `1/3pir^2h`

`pir^2h  :  1/3pir^2h  :  4/3pir^3`

The volume of a cylinder is three times the volume of a cone with equal height and radius. The volume of a sphere is two times the volume of a cone with equal height and radius. 
So the ratio of volumes is 3 : 1 : 2.