  Every closed geodesic $\gamma$ on a surface has a canonically associated knot
$\widehat\gamma$ in the projective unit tangent bundle. We study, for $\gamma$
filling, the volume of the associated knot complement with respect to its
unique complete hyperbolic metric. We provide a lower bound for the volume
relative to the number of homotopy classes of $\gamma$-arcs in each pair of
pants of a pants decomposition of the surface.
