The radius of the base of a right circular cone is $r$. It is cut by a plane parallel to the base at a height h from the base. The slant height of the frustum is $\sqrt {h^2\, +\, \displaystyle \frac {4}{9}\, r^2}$ and the volume of the frustum is $\displaystyle \frac {k}{27}\, \pi r^2h$. Find $k$.
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