Ductwork surface area calculation problem

[tibor]

Hello,

I have a major in economics and I am creating an excel spreadsheet for quotations of sheet metal ductwork as my final thesis. I need to calculate weights for various types of ductwork produced in the company I chose for my thesis. In order to calculate weight, I need to know the surface area of ductwork parts. For many parts (pipes, elbows,etc.) I have figured out the formula for surface area myself, resp. found it on the internet. But there are some pieces I am not able to figure out how to get the surface area based on the input parameters.

You will find the pictures of the parts in the pdf attachment for which I need to get the formula for calculation of the surface area (in metric units). I would be very thankful if anyone of you could help me with finding the correct formulas.

Here is the file with images and input parameters:

http://www.scribd.com/doc/91214951/Area-Calculation-Problems

Thank you very much for your time, help and effort.

Sincerely,

Tibor

[jaap]

#4, #5, #6 are truncated pyramids, so all the sides are trapeziums (or trapezoids if you're American). You should be able to work out the height of each of those trapezium sides using Pythagoras.
#10 is a cylinder of which one end is cut at an angle. If you put two of these together, you get a normal cylinder. Getting the area of the curved surface of a normal cylinder is easy, so from that you should be able to deduce the area of this shape.

The area of the others is rather more difficult, and there may not even be any closed formula for them.

[Ben-oni]

#7, #8, and #9 are just triangles and conic sections. They should be pretty easy, too.

[scarecrovv]

My first instinct would be to go weigh the parts. That way you get the actual weights, not some theoretical weight that may or may not correspond to what the people on the factory floor are building. Or even better, go ask the people on the factory floor how many of each kind of piece they can get out of a certain amount of metal. That way you account for scraps that get wasted too.

If we're doing math though, #10 is pretty easy. If you take two of those, and put the diagonal ends together, you get one cylinder of twice the size. Find the area of that, then cut it in half.