what would be the approximent dollar amount of a 5gallon jug filled with quarters?

Answer 1

I've done calculations in the past to estimate this using the thickness and diameter of a quarter, and using some guesses as to how they would pack. You can find the details on the thickness and diameter of a quarter on Wikipedia.

Mass: 5.670 g (0.182 troy oz)
Diameter: 24.26 mm (0.955 in)
Thickness: 1.75 mm (0.069 in)

For packing, the most efficient packing of circles on a plane would be in a hexagonal pattern. I forget the number I calculated using this method.

But the best way to come up with the actual number is to empirically figure it out (i.e. fill a gallon jug and multiply by 5, for example). Or better yet, *weigh* a smaller jug filled with quarters, subtract off the weight of the container, convert to grams then divide by 5.67 and divide by 4 to get the value in dollars. Use this number to estimate the value of the 5 gallon jug. I think you'll find that 1 lb. of quarters equals $20.

There will always be variation based on how the jug packs (loosely or tightly), and the actual diameter and height of the jug.

Your question made me curious, so I did some searching on the web and found a guy that actually *did* fill a real 5-gallon jug with quarters. In the end he had $4,179.50 in the jug.

Interestingly, dimes have a weight proportional to their value because dimes and quarters (and half-dollars for that matter) are made from the same materials and have the same density. They are also minted such that they have volumes proportional to their value. Two quarters would have the same volume as one half-dollar or five dimes. The net result is that 5 gallon jugs filled with dimes, quarters, half-dollars or a mixture of all three coins would have roughly the same value. There would probably be some variation favoring the smaller coins packing tighter, but otherwise they would be close to the same value.

This doesn't carry over to pennies or nickels which have different volumes and materials, but using information on their actual weights and volumes, you could probably estimate the value of a 5 gallon jug filled with pennies or nickels too.

Answer 2

first, estemate the volume of one quarter.

i just measured a quarter and the radius is roughly about 13mm. and the height is 1mm

V =(pi) (13)^2 * 1
V = 169pi mm^3

so we know that it is $0.25 dollars per 169pi mm^3

convert gallon to mm^3
1 US gallon = 3,785,411.8 mm^3
so 5 US gallon = 18,927,059 mm^3

18,927,059 mm^3 * 0.25 dollars / 169pi mm^3 = 8912.23 dollars

this is an OVER-ESTIMATION because by using this method, i assume ALL space are occupied. If you place 4 quarters next to each other, and kinda form a square, there is a hole at the center.

So i would say roughly about $7,000 - $8,000