Hi kimberu,

I think most of the helpers on this forum are averse to answering questions where the symbols used are not defined, so it would be a good idea to make your question as clear as possible. For example: what are V1,V2,h; which plane is the second plane; and splitting what into small segments?

Having said that, I think I got the gist of what you were asking: when do the upper and lower estimates of the volume of the solid converge to the same value? Well that always happens when is Riemann integrable, where is (as you defined) the cross-sectional area of the solid at height

The most important things to read about are the conditions of Riemann integrability, which returns lots of hits in google. In particular, is Riemann integrable if is continuous over the height of the solid.

And, out of interest, this is probably a calculus question, but that's beside the point really!

Hope this helps, and enjoy the rest of your course.