Heating Area for Cone Hopper

We get cone hopper dimension. I have the required height (h), initial diameter (d) & upper diameter (D).

Now we used AutoCAD for the calculation of the hopper area.

We draw a simple drawing in 2D (Figure-1).

Now we extend angular line with fillet command on initial diameter (d) side (Figure-2). we say this tentative height (H).

Now we draw a circle from center of tentative height line (Figure-3) to initial diameter edge.

Now we draw another circle from center of tentative height line (Figure-4) to upper diameter edge. This circle diameter is 2 times of tentative height.

Now we calculate maximum angle for area.

Angle (theta θ) = (D / 2H) x 360

Now we draw this angle (Figure-5) in a bigger circle.

Now we trim all unwanted lines like a triangle, other side of circles (Figure-6). 

Now we use join figure-6 and use area command & get result.