Question 1204675: How many quarters will fit in a can that is 25.5 inches circumference and 8.5 inches tall? Found 6 solutions by greenestamps, josgarithmetic, Alan3354, Edwin McCravy, ikleyn, math_tutor2020:Answer by greenestamps(13209) (Show Source):
It is not possible even to begin working on this problem without knowing the dimensions of the quarters. And there would likely by a small variation in the dimensions of those quarters.
And even if we knew those dimensions, we could only get an approximate answer, because it is impossible to know exactly how the quarters would be stacked in the can.
Let's assume the quarters are all uncirculated, in tall cylindrical
stacks, standing vertically in the can.
By Googling, I have found these facts:
1. The official diameter of a quarter is 0.955 inches.
2. The official thickness of a quarter is 0.069 inches.
3. The maximum number of non-overlapping smaller circles of
diameter d that will fit inside a larger circle of diameter D
is the integer part of
Since the circumference of the can is 25.5 inches, its diameter is
= 8.116902098 inches.
The diameter of a quarter is 0.955 inches,
so using the formula,
.
So 72 stacks of quarters can be placed in the can.
Now since the can is 8.5 inches tall, and a quarter has thickness 0.069 inches,
we see how many quarters are in each stack.
So there are 123 quarters in each stack. So we multiply that by 72 stacks
and get 8856 quarters. [worth $2214]
Edwin
You can put this solution on YOUR website! .
How many quarters will fit in a can that is 25.5 inches circumference and 8.5 inches tall?
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Let's consider these quarters packed in vertical stacks inside the can.
The diameter of the can is D = = 8.117 inches (rounded).
The diameter of a quarter is d = 0.955 inches (an official info).
= = 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 = 123 (rounded to the closest smaller integer).
So, the ANSWER to the problem's question, using this conception, is
57*123 = 7011.
Solved.
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What is remarkable and amazing, this solution (in the frame of this conception)
is exact and precise - - - not approximate ( ! )
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