Question 1204675
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How many quarters will fit in a can that is 25.5 inches circumference and 8.5 inches tall?
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<pre>
Let's consider these quarters packed in vertical stacks inside the can.


The diameter of the can     is  D = {{{25.5/3.14159}}} = 8.117 inches (rounded).

The diameter of a quarter   is  d = 0.955 inches (an official info).


{{{D/d}}} = {{{8.117/0.955}}} = 8.5.


So, the problem is reduced to this question


    +---------------------------------------------------------------+
    |        how many circles of radius 1 unit can be placed        |
    |     in the circle of radius 8.5 units without overlapping     |
    +---------------------------------------------------------------+


In the Internet, there is web-site  http://www.packomania.com/  and the calculator there 
(free of charge, for common use).


 +----------------------------------------------------------------------------+
 | It easily determines the MAXIMUM possible solution for such placing (!!!). |
 |  and even shows you a final diagram  (which is just a fantastic service)   |
 +----------------------------------------------------------------------------+


In our case, 57 circles are possible to place without overlapping.


The number of quarters in each stack is  {{{8.5/0.069}}} = 123  (rounded to the closest smaller integer).


So, the  <U>ANSWER</U>  to the problem's question, using this conception, is  

                           57*123 = 7011.
</pre>

Solved.


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What is remarkable and amazing, &nbsp;this solution &nbsp;(in the frame of this conception) 

is exact and precise - - - not approximate &nbsp;(&nbsp;!&nbsp;)