What if they are R-Pro Hydras?
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Archimedes is rolling in his grave!
The only proper way to measure the volume of a disc is to drop it in a bucker of water.
Another way to look at disc volume is to look at the disc weight. If we accept that an "average disc" will float at around 140 grams, and sink at 150 grams (no trapped air), can we accept that a disc at 145 grams will just barely sink? If so, that disc will displace 145 grams of water, which is 145 cubic centimeters. If you don't like the 145 gram number pick your own, but I think that we're easily within 10% now.
Way easier than trying to measure the volume of a disc...
Whether it's 6 or 17 million discs, will every disc need to be returned to its original owner when somebody goes diving for them?
At $1 finders fee, somebody could probably make a couple hundred dollars returning every single disc. Too bad there's not an algorithm to figure that one out.