Using methods developed by us in a previous paper on gravitational collapse, we follow the evolution of an expanding spherically symmetric zero-pressure ball of dust that starts its expansion within a black hole. The general relativistic equations for the trajectories of the geodesic particle-clocks measuring our time coordinate follow from an inverse square relation, and are formally identical with equations obtained in Newtonian gravitational theory. Within the expanding body there is an apparent horizon, related to the Schwarzschild radius associated with the trajectory of each particle-clock. Because of the existence of a region of expelled surfaces, bounded on one side by the apparent horizon, we show that the destruction of the black hole is inevitable.