When trying to make a brass ferrule (it was supposed to be wrapped around the bottom of the leg) for a missing one on a tapered round piano leg, we used paper for a template and cut and tried until it fit. This ferrule looks like what you see on a wood handle for a chisel, except it wasn't made from tubing but rather from flat brass. This took a long time and I was wondering what was the mathmatical method of figuring this out. The paper template was transferred to the flat brass plate and the resultant shape was about 3.14 times the diameter long and both of the long sides were curved slightly. This part I needed was slightly conical, about 1 inch in diameter on one end and .875 inches diameter on the other and about an inch long. When laid flat, the two sides look like they have the same center of radius and the radius looks like it might be somewhere about like 6 inches, only one more and one less in diameter.
When you make a regular cone from flat stock, it looks like a half circle. This example is similar to that except that this is only part of cone and it has a very light taper compared, for example, to a dunce's hat.
Can anybody see what I am trying to do and is there an answer that is easier than doing it by paper template? Thanks--Mike.