wow -- i have a totally different answer than anything that's been posted, but i'm pretty sure my logic and math check out. pretty good at these sorts of things.
there are NO squares involved in the cross sectional area.
perhaps this site you help people out:
http://whistleralley.com/torus/torus.htm
the cross section of a hoop is a circle. you need to use that, and the length of the shelves (as a chord) to calculate the R and r for the final equation.
i got a 5 digit number, with the sum of the digits being 23.