[HuFlungDung]

Ok, I'm a noob at sheetmetal, so this is what I understood from the post above and I propose a cone with 8" diameter base, 6" diameter top, and 6" height, like a transition from an 8" to a 6" stovepipe.
(Note: through similar triangles, the slope of the cone is 1/6, therefore the apex height for a cone with a base radius of 4 would be 24)

The 24.331 radius is the radial distance from the base of the cone to the apex as measured along the hypotenuse. I determined this graphically in CAD, but could be computed as:
A^2= B^2 + C^2
A^2= (4)^2 + (24)^2

Now in the real world, I suppose you could lay a tape along the circumference of the 24.331 radius circle, and measure out the arc length of 8*Pi, but instead I computed the angle subtended by comparing the ratio of the circumference of the base circle of the cone with the circumference of the circle having the cone apex radius:
(4/24.331)*360 = 59.184°

I might be wrong, but I did print out the thing and cut it out with scissors and rolled it. It looks right.

The picture is a bit blurred, but the blue colored area would be the flat layout, the magenta is just a side view of the desired cone.

If I have errored, please advise. Thanks.