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wiki:us_coin_value_by_volume

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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.

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 mm3 results in a desired volume of 946,353 mm3.

Specifications of US Coins

The size and mass of the coins are taken directly from the US Mint.

Denomination Value Weight (g) Diameter (mm) Thickness (mm)
Cent 1 2.500 19.05 1.52
Nickel 5 5.000 21.21 1.95
Dime 10 2.268 17.91 1.35
Quarter 25 5.670 24.26 1.75
Half 50 11.340 30.61 2.15
Dollar 100 8.100 26.49 2.00

Volume by Coin

The volume of each coin is calculated by using the formula for the volume of a cylinder:

π * r2 * thickness

Value by Volume

Following is a table similar to the previous table that shows the volume occupied by each coin along with value in cents per mm3, i.e., the denomination of each coin divided by the volume.

Denomination Value Volume (mm3) cents / mm3
Cent 1 433.2349000 0.002 308
Nickel 5 688.9787539 0.007 257
Dime 10 340.1064000 0.029 403
Quarter 25 808.9274000 0.030 905
Half 50 1,582.1770000 0.031 602
Dollar 100 1,102.2590000 0.090 723

From the data in this table, one can see that the currency value by volume for dimes, quarter dollars, and half dollars is nearly identical with approximately 3/10 of one cent per cubic millimeter.

wiki/us_coin_value_by_volume.1557413171.txt.gz · Last modified: 2024/03/05 12:58 (external edit)