I posted a reference to a paper on calculating the volume of Nurbs objects a while back. So it is possible...
The Nurbs integral calculus mathematics was difficult, or pretty nearly incomprehensible, :-) and the Nurbs formulas get manipulated,
which I think only Michael could do? (I suppose some sort of cross section estimation could be made.)

- Brian

( The old link was bad, here is another link:)
http://www.me.berkeley.edu/~mcmains/pubs/SPM2010KrishnamurthyMcMains.pdf