An interesting math question...

[Eggsnham]

Take it to a money counting service thingy.

They usually have them at your local supermarket, and they're free.

 

[Assassin Xaero]

I dunno... a lot. I have a jar I made in high school art class that is about 20-25oz, and filled with change it was about $54, and half of that was pennies, then still probably more nickles and dimes then quarters...

 

[flipsalty]

One dollar Bob. Actual retail price, 3 dollars.

 

[tunderball]

I love how much random stuff gets asked on the Escapist, you'll never be able to work it out because the quarters will be arranged differently leaving gaps in between the coins. Also to make things even more complicated in that respect the weight of the coins would in theory push the coins flatter and more compact towards the bottom. So not only would you have to calculate how many quarters fit in a litre bottle, you'd then also have to do a complicated calculation that accounts for weight...
Or you could just count it??

 

[delanofilms]

The only way to calculate this is to determine the PRECISE packing efficiency of quarters.

 

[kiwi_poo]

The are two ways to do this easily:

1. how many coins can be fitted flat on the surface? multiply that with how many coins it takes per column to reach the top, plus how many more fit in the top till the lid, depending on the shape of the bottle.

2. put quarters all along the sides in a vertical fashion, then coninue doing that in a spiral till you reach the middle, where you should stack four-six quarters on top of eachother and put them in the middle. reapeat this prosess till you reach the top. (if there's a neck of any kind, you use option 1 till filled.)

all in all I suppose you could have about 200 - 300 dollars in there.

 

[ArchAngelKira]

Zetta slow

 

[Celtic_Kerr]

So i have this jar of quarters i have in my room. it's not even close to a fraction full, i think it has like 8$ worth in there. Now here's the question, the bottle can hold 64 oz. of liquid, how many quarters can fit in a bottle like that and how much money will it be when its full? honestly i have no idea thats why i came here

THis is a very difficult question, as it depends on the placement of quarters within the jar. Sometimes you can gert more money than last time if they all lay flat and none are on their side. Weigh your quarters until you have an oz of quarters. Then you'll multiply that by 64 and that's the IDEAL amount

If you work in terms of volume, use a measuring cup that using "oz"

EDIT: Ridonculous Ninja Ninja'd me... Well played...

 

[arkady]

Consider an infinite number of circles of diameter D. These circles can be laid on an infinite 2D plane. For optimum packing efficiency, the centre of each circle will coincide with the centre of a tessellating pattern of regular hexagons (think honeycomb). The hexagon's shortest distance across = D. (Or 2r).

The area of each hexagon is given by 6 x (r)^2 * tan(30deg) = (6/sqrt(3))*r^2 = 2*sqrt(3)*r^2

The area of the circle is then pi*r^2.

Area circle / Area hexagon = pi*r^2 / 2*sqrt(3)*r^2 = (pi/2*sqrt(3)) = 90.7%


The packing efficiency of your quarters into a jar won't be far off this. I suggest you measure the volume of a quarter, then do:

Volume of jar / Volume of quarter.

This gives you 100% packaging efficiency. You won't quite make the full 90.7% (because I've assumed infinite plane, etc...) but if your jar is reasonably wide you'll get close to it. It depends on how many coins intersect the edge of the jar.

At any rate - I have a value of 809 mm^3 as the volume of the quarter, and you give me 64 floz for the volume of the jar.

64floz = 1893000 mm^3.

So at 100% packaging efficiency: 2341 quarters, so around 2100 at 90% efficiency. (Which is $525).

The full maths is pretty complicated, but with a simplifying assumption you can actually make it rather trivial.

 

[Flauros]

check this out.

Take out the quarters and count them in stacks of four, if thats convenient.

BAM

your mind is blown.