suppose a sphere and a cone share the same radius and the same height which is twice the radius which ratio describes the relationship between the formulas for the volume of a cone to the volume of a sphere?

The ratio that describes the relationship between the formulas for the volume of a cone to the volume of a sphere in this case is 1:3.

right for 1 but wrong about 3

Apologies for the mistake. The correct ratio that describes the relationship between the formulas for the volume of a cone to the volume of a sphere in this case is 1:2.