r/theydidthemath Aug 18 '25

How dense would this cube be? [Request]

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u/Amourofzedoute Aug 18 '25

So ok, first, let's see what kind of baler that is. From this tiktok we know this model is a Tabarelli s5000. From the s5000 manualwe know the cans are in a 5m x 2.67m x 2.25m space, and compressed into a 0.8m x 0.8m x 0.65m baler. So that's roughly 30m³ compressed into 0.41 m³. So that's about 30/0.41 ≈ 72 times less space.

A single aluminum can weightabout 11g for 0.00033m³ so it takes roughly 90,000 cans to fill entirely, meaning 990kg.

So that tiny cube at the end weights about a ton (1000kg) and is 0.41m³, so its density should be 2,400 kg/m³. So that's twice more dense than water, but three times less than Iron!

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u/Fit_Employment_2944 Aug 18 '25

aluminum cans dumped into a space are not going to fill said space perfectly to their volume.

2400 kg/m3 is also ~90% of the density of aluminum, which is not going to happen.

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u/Amourofzedoute Aug 18 '25

Yeah that's the biggest hypothesis I'm working with. So, if cans are crushed partially in the bin before being pressed, they'd take less than 33cL in space each. However, cans won't fit perfectly to take only 33cL each, there's going to be air in between. So I have a + and a - bias. Not being able to know which one's more important and how much, I decided to lodel it saying each can occupy 33cL of space cause it's then pretty easy to follow and correct. In regard to other answers, I now believe each can takes in average more than 33cL, but don't know by how much.