[tolo]

And also the surface area of a spherical zone, as shown here: http://mathworld.wolfram.com/Zone.html

[svrocks]

After choosing a different way to find the angle, my answer matches yours. Kudos for having a much simpler answer.

[svrocks]

wow that's an interesting and counterintuitive result. I need to figure out why my integral doesn't line up with that