Hi Renoir,

I think the basic principles are simple, but the question would be, what is the basic data.

For instance, using a little bit of calculus it seems obvious that the surface area is the average of the inner and the outer arcs, times the length of the line that connects them - just like the formula for a figure with two parallel sides. (Imagine dividing the figure into many small pieces, by projecting radii from the centerpoint - each one would have two almost straight and parallel lines, opposite each other.)

However, do you have this information? i.e., the length of the two pieces of circle. Or do you start with some other information?

>a'm also a bit of a mechanical type of guy. I'm thinking that if I know that the diameter of the top circle needs to be 2" and the height of the cone is 10", then I could lay a piece of paper out, draw a 2" circle at the top, go down the paper 12" and draw the bottom part of that circle using the same center point for the (very large) compass. Then just draw straight lines tangent to the sides of both circles, then I would have my shape. But it sounds too easy.
>
>>I am in little bit of a hurry right now, but I think the basic principle is as follows. You would have to extrapolate the figure to where the two straight lines intersect. Then you have two pies, a large one, from which you have to deduct the small one (the cut-off tip). For each of the pies, the formula would be pi() * r^2 * (degrees / 360). (Note: pi() * r^2 is the formula of the circle, so you are getting a fraction of a circle here.)
>>
>>HTH,
>>
>>Hilmar.
>>
>>>Picture a narrow cone with the top lopped-off. More like a tower, but the bottom circumference is larger than the top. Ok, a lighthouse. Now, cut it down the side and lay it out flat. Basically it would be something like a rhombus with a concave top and a convex bottom. How could I calculate/create that design knowing the dimensions I want my final shape to be? Something like this:
>>>
>>>

>>>
>>>                    .      .
>>>                   . ` .. ` .
>>>                  .          .
>>>                 .            .
>>>                .              .
>>>               .                .
>>>              .                  .
>>>               .                .
>>>                 .           .
>>>                     `   `
>>>
>>>