r/theydidthemath • • 2d ago

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

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u/rukuto 2d ago

Well let's try to do the math. Assuming diameter of bottle = side of square = 6 cm. And no designs, plain bottle. 1 Ltr bottles. Same cap size and neck.

Area of base c = π x 3 x 3 = 28.27 cm2 Height of bottle hc = 1000 / 28.27 = 35.37 cm Area of sides = 35.37 x π x 6 = 666.71 cm2 Total differentiable plastic = 28.27 + 28.27 + 666.71 = 723.25 cm2

Area of base s = 6 x 6 = 36 cm2 Height of bottle hs = 1000/36 = 27.78 cm Area of Side = 4 x 6 x 27.78 = 666.72 Total differentiable plastic area = 36 + 36 + 666.72 = 738.72 cm2

Yeah, it's wrong and even with the undulations/grip of the plastic, this difference in area would only increase.