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 Question from sheri: I need to estimate how many pieces of metal are in a container that is 3 feet by 3 feet and 2 feet high. the metal pieces are 1" round and 1/2 centimeter thick. I've never been any good at math. please help. thanks, Sheri

First, you have to understand that such pieces cannot completely fill the container. They will probably fill it more efficiently if they are neatly packed; the most efficient packing for a large container is if, within each layer, each row is offset half a space against its neighbours:

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For a very large array this gives a "packing fraction" of pi/(2*root 3) which is about 90.6%. That means that for every liter of internal volume you have 906 cm^3 of metal and the rest is air. For small containers optimizing packing near the edges may be more important.

When you write `1" round' do you mean "round and 1" across", "round and 1" in radius" or "round and 1" in circumference?" I'm going to assume the first. 1" is about 2.54 cm so that's a 1.27 cm radius and a volume of pi r2 h = 2.53 cm3. Dividing by the packing fraction, each cylinder actually needs about 2.8 cm3 living space.

Now, 3x3x2 ft3 is about 510 000 cm3 [use Google for unit conversions!] which is enough space for about 180 000 cylindrical slugs.

-RD

PS: A rougher but easier estimate: a square packing arrangement

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gives

(3x12) * (3x12) * (2*5*12) ~ 155 000 slugs.

Good Hunting,
RD

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