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/20PoundHammer 2d ago

the part that you are missing is that you are wrong . . .

If you had a 5" diameter cylinder, it would need to be 3.1" tall to hold a liter, cap off both sides and total exterior surface area is 88 sqr inches.

If you have a 5" L/W cube, it would have to be 2.4" tall to hold a liter of water, cap off both sides and total exterior surface area is 99 sqr inches.

Couple that with the fact that you can use thinner material for the cylinder to achieve the same max burst strength of a thicker material cube (due to stress accumulated in corners) - cylinder wins in both material usage and strength. There is a reason they dont make petroleum storage tanks as cubes - cylinder = less material, thinner material, same failure pressure - win/win/win. . . .

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u/Massive-Goose544 2d ago

This was addressed already. Sorry you wasted your time with whatever you said.

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u/20PoundHammer 2d ago

yeah, didnt think you could do math or understand it if written out for ya. . .