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A quarter is 808.5 mm3. If you melted the quarters into a slurry, and poured that into the barrel, you could fit 208 million/808.5 = 257,000 quarters into a 55 gallon drum.

If you want to preserve them whole, this becomes a stacking problem. There will be spaces between the quarters, and we would have to estimate how much space is wasted. Just drawing packed circles on a piece of paper I'd guess perhaps 10% of the volume would be air, so deducting 25,000 quarters from our solid mass gives a ballpark estimate of 225,000 quarters.

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Q: How many quarters will fill a 50 gallon barrel?
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