A right circular cone, a right circular cylinder and a hemisphere, all have the same radius

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder equal their diameters. Then their volumes are proportional, respectively to

  1. 2 : 1 : 3
  2. 3 : 2 : 1
  3. 1 : 2 : 3
  4. 1 : 3 : 1

Answer

Let the radius of the cone, cylinder and hemisphere be r.

The height of cone and cylinder is 2r.

Volume of a cone = (1/3) πr22r = (2/3) πr3

Volume of cylinder = 2πr3 

Volume of hemisphere = (2/3) πr3

The ratio of volumes is 1 : 3 : 1

The correct option is D.