If the box isn't terribly large, it could be made of wood and turned on a lathe. For better stability, it could be made using fiberglass, laid over an inflated ball with the ball deflated and removed after it sets. a flange for mounting the driver would be attached and glassed in- as long as it's fastened securely to the shell and assuming the shell is thick enough, it should be resonance-free since a sphere is an inherently rigid form.
FYI- V=4/3Πr³