User Tools

Site Tools


wiki:us_coin_value_by_volume

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision
Previous revision
wiki:us_coin_value_by_volume [2019/05/09 11:22] gregorwiki:us_coin_value_by_volume [2024/03/05 13:13] (current) – external edit 127.0.0.1
Line 1: Line 1:
 ====== Value of US Coins by Volume ====== ====== Value of US Coins by Volume ======
-The task is to fill a 32 fluid ounce bottle with coins that "//silver//", i.e., no one cent pieces.+The task is to fill a 32 fluid ounce bottle with coins that are "//silver//", i.e., no one cent pieces.
  
 For these calculations, all values have been converted to metric - grams and mm - and the final weight is presented in both kilograms and pounds. For these calculations, all values have been converted to metric - grams and mm - and the final weight is presented in both kilograms and pounds.
  
 Converting 32 fl. oz. to mm<sup>3</sup> results in a desired volume of 946,353 mm<sup>3</sup> Converting 32 fl. oz. to mm<sup>3</sup> results in a desired volume of 946,353 mm<sup>3</sup>
 +
 +===== Summary =====
 +The lowest value option is the result of filling the vessel exclusively with nickels. This results in a theoretical maximum value of $68.68, but a more realistic value of approximately $27 due to the space between the coins.
 +
 +The highest value option results from filling the vessel with dollar coins for a theoretical maximum of $858.58, but a more realistic value of approximately $343.
 +
 +**The more likely scenario is a mix of nickels, dimes, and quarters. Assuming an even distribution of all three denominations results in a theoretical value of $205.95 with a more realistic value of approximately $82.**
  
 ===== Specifications of US Coins ===== ===== Specifications of US Coins =====
Line 67: Line 74:
  
 ^ Denomination      ^ Value        ^ Volume (mm<sup>3</sup>) ^ Coins ^ Derated ^ Value ^  ^ Denomination      ^ Value        ^ Volume (mm<sup>3</sup>) ^ Coins ^ Derated ^ Value ^ 
-| Cent              |            |     433.2349000 |  2,184 |    873 | $  8.74 ^ +| Cent              |            |     433.2349000 |  2,184 |    873 |   $8.74 ^ 
-| Nickel            |            |     688.9787539 |  1,373 |    549 | $ 27.47 ^+| Nickel            |            |     688.9787539 |  1,373 |    549 |  $27.47 ^
 | Dime              |          10  |     340.1064000 |  2,782 |  1,113 | $111.30 ^ | Dime              |          10  |     340.1064000 |  2,782 |  1,113 | $111.30 ^
 | Quarter                    25  |     808.9274000 |  1,169 |    467 | $116.99 ^ | Quarter                    25  |     808.9274000 |  1,169 |    467 | $116.99 ^
 | Half              |          50  |   1,582.1770000 |    598 |    239 | $119.63 ^ | Half              |          50  |   1,582.1770000 |    598 |    239 | $119.63 ^
 | Dollar            |         100  |   1,102.2590000 |    858 |    343 | $343.42 ^ | Dollar            |         100  |   1,102.2590000 |    858 |    343 | $343.42 ^
 +
 +===== Evenly Distributed Nickel, Dime, Quarter =====
 +As one cent pieces are excluded from consideration and both half dollar and dollar coins being less common, consider the condition where the an equal number of nickels, dimes, and quarters are deposited into the vessel.
 +
 +One may arrive at an aggregate volume value for these three coins by adding the individual volumes together:
 +
 +688.9788 + 340.1064 + 808.9274 = 1,838.0126 mm<sup>3</sup>
 +
 +and the aggregate value of this virtual coin is the sum of the values of the individual coins:
 +
 +5 + 10 + 25 = $0.40
 +
 +Dividing the volume of the virtual coin into the volume of the vessel results in 514 of the $0.40 coins for a value of $205.95.
 +
 +Derating the quantity of coins to only 40% of the theoretical maximum number of virtual coins results in 205 total virtual coins at a value of $0.40 for a tital value of $82.38.
 +
 +The resultant table for individual coins and the virtual coin - the more realistic distribution of coins - is shown here, without any derating, so that the reader may use whatever density derate is desired.
 +
 +^ Denomination      ^ Value        ^ Coins ^ Maximum Value ^ 
 +| Cent              |           1 |  2,184 |    $21.84 ^
 +| Nickel            |           5 |  1,373 |    $68.68 ^
 +| Dime              |          10 |  2,782 |   $278.25 ^
 +| Quarter                    25 |  1,169 |   $292.47 ^
 +| Half              |          50 |    598 |   $299.07 ^
 +| Dollar            |         100 |    858 |   $858.56 ^
 +| Virtual 5/10/15            40 |    514 |   $205.25 ^
 +
 +===== Weight =====
 +Purely as a thought experiment, the total weight of the vessel for each coin may be calculated. These values assume the theoretical maximum number of coins and should be derated as necessary to account for the spaces between the coins:
 +
 +^ Denomination      ^ Value        ^ Weight (g)^ Coins ^ Mass (Kg) ^ Weight (lbs) ^
 +| Cent              |           1 |     2.500 |         2,184 |  5.46 |  12.0 |
 +| Nickel            |           5 |     5.000 |         1,373 |  6.87 |  15.1 |
 +| Dime              |          10 |     2.268 |         2,782 |  6.31 |  13.9 |
 +| Quarter                    25 |     5.670 |         1,169 |  6.63 |  14.6 |
 +| Half              |          50 |    11.340 |           598 |  6.78 |  15.0 |
 +| Dollar            |         100 |     8.100 |           858 |  6.95 |  15.3 |
 +| Virtual 5/10/15            40 |    12.938 |           514 |  6.65 |  14.6 |
 +
 +
  
wiki/us_coin_value_by_volume.1557415338.txt.gz · Last modified: 2024/03/05 12:58 (external edit)