This is an old revision of the document!
Table of Contents
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.