What is the most accurate way to estimate the surface area of a cylindrical bottle that decreases in diameter from its wides point (the body) to the narrowest point ( the neck and cap)? It seems like we did similar problems in calculus, however: 1. I don't remember any of it, and 2. I think you were always provided with the mathmatical expression of curve of the bottle so that you could calculate it by rotating it around the center axis or something. I just have the actual physical bottles in front of me and want to know what the outer surface areas are. My best guess so far is to just treat them as cylinders and not take into account the curved surface where it transitions from the body to the neck, but I would like to be as accurate as possible. Is there some correlation between displacement of water and surface area I could calculate by dunking them? Any and all suggestions are appreciated.