Know of anyone that has a large bandsaw? I cut apart an ancient Ebonite Tornado (the rubber variety) a while back with this method and found no core, but there did seem to be a distinct 1" thick "coverstock" surrounding a black filler "core"
If you use this method, be careful! We all know that finger loss and bowling don't go hand in hand.
Another option could be a reciprocating saw with a blade longer than the balls width, but blades such as these will be probably run $15-$20 for a 5 pack.
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"A word to the wise ain't necessary -- it's the stupid ones that need the advice." Bill Cosby
"Never argue with an idiot. They bring you down to their level and beat you with experience."