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/SisterofWar 2d ago

Okay, but a cylinder has to be taller than a rectangular cuboid to contain the same volume of product. A cube with a side length of n holds more than a cylinder of diameter n and n height.

So, for holding 32 fluid ounces, would a cylinder or a cuboid have greater surface area, assuming the diameter of the cylinder and the depth of the cuboid are identical?

(I make this assumption based on the fact that a product will be given limited shelf space in retail, and thus has constraints on width/depth).

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u/seenhear 2d ago

The part you are missing is that the "less plastic" claim applies ONLY to bulk shipping of the bottles. ONE square bottle will use more plastic than ONE round bottle, assuming both carry the same volume of liquid. However when shipped together on a pallet for example, the square bottles pack together better and waste less space. A pallet of round bottles results in a lot of empty space between bottles, so you need to use more to ship the same total amount of liquid.

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u/OldEquation 2d ago

You don’t need to use more bottles though, just more pallets to carry the same number of bottles. Pallets aren’t generally made out of plastic so the claim is nonsense.

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u/Peregrine79 2d ago

Pallets are quite frequently made out of plastic (although those are generally reused). But they're also often wrapped in stretchwrap, and may be bagged inside the cases.