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Making use of the dual Bonahon-Schl\"afli formula, we prove that the dualvolume of the convex core of a quasi-Fuchsian manifold $M$ is bounded by anexplicit constant, depending only on the topology of $M$, times theWeil-Petersson distance between the hyperbolic structures on the upper andlower boundary components of the convex core of $M$.

The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance