The powerful Fanaroff–Riley class II ( FR II ) radio galaxy Cygnus A exhibits primary and secondary hotspots in each lobe . A 2 Msec Chandra X-ray image of Cygnus A has revealed an approximately circular hole , with a radius of 3.9 kpc , centered on the primary hotspot in the eastern radio lobe , hotspot E. We infer the distribution of X-ray emission on our line of sight from an X-ray surface brightness profile of the radio lobe adjacent to the hole and use it to argue that the hole is excavated from the radio lobe . The surface brightness profile of the hole implies a depth at least 1.7 \pm 0.3 times greater than its projected width , requiring a minimum depth of 13.3 \pm 2.3 kpc . A similar hole observed in the 5 GHz Very Large Array radio map reinforces the argument for a cavity lying within the lobe . We argue that the jet encounters the shock compressed intracluster medium at hotspot E , passing through one or more shocks as it is deflected back into the radio lobe . The orientation of Cygnus A allows the outflow from hotspot E to travel almost directly away from us , creating an elongated cavity , as observed . These results favor models for multiple hotspots in which an FR II jet is deflected at a primary hotspot , then travels onward to deposit the bulk of its power at a secondary hotspot , rather than the dentist drill model .