Size of Material required to cut out a truncated cone

Amplegirthage

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Apr 9, 2024
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Hi, Im hoping the brightest assembled minds of the interweb might be able to help me with geometry problem Im trying to solve at work.
We manufacture tapered conical connectors. Which we sew up out of fabric.
I'm trying to come up with an excel pricing sheet to estimate the amount of material required to make one of these connectors.

Connector would look something like this : and when unfolded like this :
Truncated cone.jpg Flat pattern.jpg

Im trying to work out how much material is required to cut one out. Like this :
flat pattern and material.jpg

We have some variables:
Diameter of the top of the cone
Diameter of the bottom of the cone
and the Height. ( Typically these might be 500mm top dia x 350mm bottom dia x 300mm high)

So in the spreadsheet I want the user to enter these dimensions.
I want the calculation to work out the length and width of the material required. From there I can work out the price.
Its got me stumped :oops:
 
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