My mom is collecting pennies in an old glass milk jug, and we just recently got the halfway mark. But figuring out how many pennies are in the jar fries my brain. I'm not looking for an answer accurate to the cent, but a rough estimate would be cool to have. As it is, I think a dime made it in, so it'll never be 100% anyway.
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The shape of a penny is not a standard shape, so there isn't an agreed upon packing density (how efficiently the space is filled with pennies). A very similar post shows an empirical packing density of ~57% for a US penny, so of 2.5 gallons, only 1.425 gallons is taken up by penny. The US penny is 0.75 inches in diameter and 0.0598 inches thick, so the volume works out to:
pi*(0.75/2)^2 * 0.0598 = 0.02642 in^3
1.425 gallons is 1.425 gal * 231 in^3/gal = 329.175 in^3
Dividing these numbers giver number of pennies:
# pennies = 12459.86 pennies or about $124.60
I bet I could fit more
Well each gallon with the volume fully filled by pennies would be 11314 pennies, but with the air pockets in between them they can fit around 8000 pennies in each gallon. So that would be around 20000 pennies in all of those 2.5 gallons, therefore you should be looking at around $200.
STEP 1: weigh the jar full of pennies. Note the number.
STEP 2: dump all the pennies out
STEP 3: weigh the empty jar. Note the number.
STEP 4: weigh 10 random pennies from your pile, don't take them all from the same spot, and find the average weight by adding their individual weights together and dividing by 10. Note the number.
STEP 5: take the number from step 1 and subtract the number from step 3 then divide by the number from step 4. (S1 - S3) ÷ S4 = roughly how many pennies you have. Divide again by 100 to get the value in dollars ± a penny.
See more: Question: How Far Is 100 Meters On A Track And Back, How Long Is 100 Meters On A Track
STEP 6: put all the pennies back before mom finds out.
And they said math has no real world applications
Created Apr 26, 2013
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