Approximately how much money would be in a five gallon jar full of nickels
dimes and quarters?  Assume equal amounts of each coin.  Please
explain answer.

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Request for Question Clarification by websearcher-ga on 11 Sep 2002 12:57 PDT

Hi killerhippo-ga:

It's unclear from your question whether you are looking for the total
*weight* of the coins or the total *value* of the coins - or both. :-)

Please clarify. 

Thanks. 

websearcher-ga

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Clarification of Question by killerhippo-ga on 11 Sep 2002 13:00 PDT

Sorry, you are right...I am looking for the value of the money not the weight.

A five gallon (liquid, US) container is equivalent to 3785411.784
cubic millimeters. In practical application, it is probably somewhat
less, because the jar may or may not have a neck or other area where
coins can't fit.

The dimensions of a nickel, dime and quarter are approximately the
following:

nickel      21.2 mm diameter,  1.95 mm thickness
dime        17.9 mm diameter,  1.35 mm thickness
quarter     24.3 mm diameter,  1.75 mm thickness

The formula for volume of a cylinder is V = (PI)r^2h. That makes the
volume of the coins the following:

nickel     688.3 cubic mm
dime       339.7 cubic mm
quarter    811.6 cubic mm

If we take the average of the three coins (by summing the volumes and
dividing by the number of coins) we get an average volume of 613.2
cubic mm.

If we divide the volume of the container (3785411.784 cubic mm) by the
average volume of a coin (613.2 cubic mm) we get 6173 coins. Saying
that there is an equal number of each denomination, we divide by three
which gives us 2057 coins of each type. If we multiply by the value of
each coin we get:

nickel     2057 * .05 = 102.85
dime       2057 * .10 = 205.70
quarter    2057 * .25 = 514.25

Summed together, this gives us a grand total of $822.80.

CoinStar estimates that a 1 gallon container holds about $160.95 of
mixed coins, so this is probably a pretty close approximation. In
practical application, you always have some airspace between the coins
so a real container, again, most likely holds slightly less than this
much.

Let me know if you need anything more.

Happy coin counting!



Digital Dutch Unit Convertor
http://www.digitaldutch.com/unitconverter/

Distraction, US Coins
http://www.penscil.com/Distraction.html

Area and Volume of Solids
http://library.thinkquest.org/20991/geo/solids.html

CoinStar
http://www.coinstar.com/coinstar2/cswebframe.nsf/GoHome

Search Strategy:
unit conversion
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coin dimensions nickel dime quarter
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=coin+dimensions+nickel+dime+quarter

formula volume cylinder
://www.google.com/search?hl=en&ie=ISO-8859-1&q=formula+volume+cylinder

Very good...and quick..Thank you.  Exactly what I was looking for.