The radius of a sphere is equal to the radius of the base of a right circular cone

The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is

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

Answer

Let the radii of the sphere and the cone be r. Since volume of sphere is twice that of the cone, we have

4/3 πr3 = 2×(1/3 πr2h)

⇨ 2r = h

⇨ h : r = 2 : 1

The correct option is C.