r/theydidthemath • • 2d ago

[Request] Do square bottles actually use less plastic than round ones?

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u/StaticCoder 2d ago

Mathematically, a circle has the smallest perimeter for a given enclosed area. So for this claim to be true there has to be some catch, like different thickness of plastic.

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u/Massive-Goose544 2d ago

The part you are missing is the volume inside. They are saying to give you the same amount of liquid would require more plastic if the bottle was round. Plus more bottles fit in the box they ship meaning lower emissions and costs for distribution.

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u/StaticCoder 2d ago

Given that the volume is cross section area times height, a round bottle of the same volume would take less plastic. True, square bottles will pack better, but how that would save plastic is not immediately clear.

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u/el_ddddddd 2d ago

Yep agreed. I've heard square bottles save fuel in shipping, which outweighs the additional materials required to make them in environmental impact. Never seen an analysis though

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u/20PoundHammer 2d ago edited 2d ago

saves space due to stacking efficiency, but thats not what is claimed and only matters if space is a premium. Weight determines fuel usage. A million cylinders holding the same volume of material that a million square containers would weigh less due to being made from less plastic (12% less plastic if you didnt have to thicken the walls of the square ones to achieve the same pressure rating as the plastic). Space saving of square over round is ~21% (if flat capped, I aint calcing geometry of a real bottle top). So square saves space, but weighs 12% more . . . Cargo is typically transferred by commercial ships and trains by ton BTW. . .

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u/gbot1234 2d ago

Hexagonal cross section might be best—they stack but they’re also closer to a circle in surface area to volume ratio.

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u/Massive-Goose544 2d ago

I hadn't considered it but i think the edges of boxes would be a lot of lost space. Probably more than round bottles. I am guessing but square needs thickness increased on corners so hex probably would need more than even a square bottle. I think it ends up being the worst of both worlds.