>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.

You need to know the radius of the imaginary circle from which you're cutting this out. That radius would be the distance between the outer edge of the bottom of the cone, to the top of the full cone (i.e. where it would be if it wasn't chopped off).

First you need the height of such a full cone. You can do that as a proportion: UpperRadius/LowerRadius=ChopHeight/TotalHeight (1)

ChopHeight=TotalHeight-ChoppedConeHeight

From your text above, LowerRadius=?, UpperRadius=1, ChoppedConeHeight=12.

This reduces to a simple linear equation with one variable. Now that you got the height, the radius of the big circle would be the diagonal of a triangle, where the cathetes are TotalHeight and LowerRadius.

So you draw two circles - one of this big radius, and another one with radius proportionately smaller (just the same ratio as in the proportion (1)).

Now you only need to calculate the angle of this circle (actually the ring between the inner and outer circle) to cut out. Calculate the circumference of the lower circle and divide that with the circumference of the big circle you're cutting. Multiply the result with 360 and there you are.