I think it's similar to calculating arc length. The surface area of a small slice of width dx is . You have and . So you integrate , which comes out to 21.322.
For this question: http://i62.tinypic.com/2uh70xw.jpg I've been stuck for a while. I'm used to finding area using a cross section but is my surface area answer right? I'm not sure about it (Just for participation points, doesn't count if I get it right but I want to know if I'm doing it right) Can you take me through the steps and did I come up with the right answer?