Circle $O$ has radius $r$ and diameter $d = \overline{AB}$. The circle is curved so that it forms part of the surface of a cylinder and point $A$ touches point $B$. The locus of all lines $\overline{PQ}$ such that points $P$ and $Q$ are on circle $O$ and $\overline{PQ}$ is parallel to $d$ is now drawn in, forming a closed shape. What is the ratio of this shape’s volume to $r^3$?