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Great one, John! :D

I guess Xhris' name is not John? Is it?

Isn't it easier to make a trivial calculation (see the file attached to my previous post) then?

I think the bast way is to combine these two methods. The first part form jeffb is simpler. But we still need some math for label length.
Here how this can be done.

Jeffb, your method is approximate. It is not precise. In your illustration it's quite clearly visible that the perimeter of the wide end of the cup is longer than the long side of your label....