Thread: Derive the Volume of a Cap of a Sphere Using Integrals

Hey everyone, I'm trying to derive the formula for the volume of a cap of a sphere. The sphere has radius "r" and the height of JUST THE CAP is "h." The only thing that I can think to do is revolve an arbitrary 2D shape around the x-axis, making a cap with the limits of integration from r-h to r. It sounds very complicated though and I'm having lots of trouble with it. Can anyone give me some ideas? THanks

It's not as bad as it seems.