# Filling An Ice Cream Cone

Geometry Level 4

A right circular cone with a vertex angle of $$30^{\circ}$$ is opened upward. A sphere with a radius $$r$$ is dropped into the cone. A second sphere, this one with a radius $$R$$, is placed on top of it. The second sphere rests in contact with both the bottom sphere as well as the sides of the cone (all the way around). What is the ratio $$\dfrac Rr$$?