How to calculate surface area of a curved plane? could anyone explain how to calculate the surface area of a curved plane?  I am trying to calculate the surface area of a "vaulted" ceiling that is 24' long, 7' wide, and the height of the curve is 4' at the mid-point so that I can figure out how much paint I need to buy.
Here is an illustration:  

If it were a simple flat ceiling, I would just multiply length x width, but that's not what I have here and a google search is leaving me empty-handed.  Any ideas?
Thank you very much!
-Neal

use the formulae you derived in part 1 to calculate the curved surface area and the total surface area of the cylinder given below
