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 :

Let the radius of cone and the sphere be R and the height of the cone be H
Volume of sphere $$ = \frac{4}{3}\pi {r^3}$$
Volume of cone $$ = \frac{1}{3}\pi {r^2}h$$
According to given information :
$$\eqalign{ & \Rightarrow \frac{4}{3}\pi {R^3} = 2 \times \frac{1}{3}\pi {R^2}H \cr & \Rightarrow 4R = 2H \cr & \Rightarrow \frac{H}{R} = \frac{4}{2}\,Or\,2:1 \cr} $$