I'd like to build a small hot-air balloon out of flame-retardant plastic sheeting to suspend a camera. The plastic sheeting (plastic film) is commonly sold in a long roll in a width of 20ft (6 meters).
Given an unlimited amount of this film (which for math purposes is just the same as paper) with maximum width of 6 meters, how can I build a balloon with a hole at the bottom (what is the most general mathematical name for a balloon?) with the least total length of seams (reduce the chance that I mess up when melting the plastic together)?
Assume I am willing to cut ANY shapes out of this material and I'm willing to use as much of it as necessary to achieve the least total length of seams. But the constraint is: the width is maximum of 6 meters. Obviously answers to this question are dependent on the balloon volume; something around 100 cubic meters should be enough, but I would like to find a general answer to the question.
The balloon can really be any shape you want including funny ones...it could even be a cube for all I care. It just has to hold a volume of air!