A right circular cone and a right cylinder with the same height $20$ do not have the same circular base, but the circles are coplanar, and their centers are the same. If the cone and the cylinder are on the same side of the plane and their base radii are $20$ and $10$, respectively, find the ratio of the volume of the part of the cone inside the cylinder over the volume of the part of the cone outside the cylinder.

Let's think step by step and output the final answer within \boxed{}.
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