"Prakhar" wrote in message <io8rdg$5bb$1@fred.mathworks.com>...
> How do you calculate area of surface of revolution of 3D curve? Though using integration I am able to calculate the area, but I would like to know a simpler method such as Pappus theorem for 2D curve.
>
> Is the Pappus theorem limited to 2D curve or is the generalisation of Pappus theorem for 3D curve available?
>
> I would also like to know that is there a theorem which says that the line about which surface of revolution of a given curve has minimum area should pass through the centroid of the curve?
         
Given the axis of revolution, transform curve point coordinates to cylindrical coordinates using that axis as the zaxis. Then the curve of z and r (regarding r as always positive,) and ignoring azimuth, would constitute a twodimensional curve and the Pappus centroid theorem would apply to that. However it means finding the 2D centroid and the total 2D arclength along this 2D curve which would surely require some kind of integration. This 2D arclength is not the same as the original curve's 3D arclength. At least a onedimensional integration seems inevitable.
Roger Stafford
