• Fleur_@aussie.zone
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    5 days ago

    Volume of glass

    Volume of hazelnuts (median)

    Packing efficiency of spheres in a cylinder

    Do some math

    Be wrong by an order of magnitude because all the little hazelnuts are concealing one giant one

  • Gustephan@lemmy.world
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    5 days ago

    Vibes. I look at it and try to guess and submit a number within 5 or 10 seconds. It may not be as accurate but I feel like I get more benefit training my ability to estimate at a glance than I do training my ability to do math and spatial reasoning assisted by math. Im already really good at math and math assisted spatial reasoning

  • jh29a@lemmy.blahaj.zone
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    5 days ago

    I counted 11 down and 7 across, so I assumed the radius is 3.5 hazelnuts and the height eleven, making pi r² h = 423 hazelnuts. that is, if they haven’t snuck in any walnuts.

  • ornery_chemist@mander.xyz
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    6 days ago

    Roughly a truncated cone with diameters ~7 nuts and ~9 nuts, and the cup is ~12 nuts high (quite hard to tell due perspective and nits of different sizes). Throw in an extra layer to account for the heap at the top (which is a dome, but the dome is taller than 1 hazelnut, so treating it as a shorter layer should give some error cancellation) to give a height of 13. The volume using the formula for a truncated cone of those dimensions is ~657 cubic hazelnut diameters. Random sphere packing is 64% (though wall effects should decrease this number) giving a total of 420 nuts (nice).

    Answer

    This ends up being about 5% lower than the true answer. I’m surprised it’s that close. This is in the opposite direction from what I expected given wall effects (which would decrease the real number relative to my estimate). Perturbing one of the base diameters by 1 nut causes a swing of ~50, so measurement error is quite important.

  • Caveman@lemmy.world
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    6 days ago

    I’m going to guess the cup is around 12 nuts high and 5 nuts in diameter at the center.

    Let’s assume it’s a cylinder to get the volume (2/5)^2 * pi * 12 as the volume or around 236 nuts.

    The packing density of a sphere is 74% but the edges do play a factor so nudge it down by a bit to get 70%

    So I’m going to guess 165 nuts.

  • Pulptastic@midwest.social
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    6 days ago

    The cup is about 13 hazelnuts high. The top circumference looks like it could hold about 24, the bottom about 20, so I’ll average that to 22.

    13*22=286

  • Wolf314159@startrek.website
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    6 days ago

    I’d ask a couple thousand people to guess in private. So the most popular answer would probably be either surprisingly close to correct or Cuppy McHazelnutface.