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.

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

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

π * r² * thickness

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.

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, whereas a nickel has less than ¹/₄ the value per volume of the other three coins and a dollar coin has approximately three (3) times the value per volume. The lowly one cent piece comes in at ¹/₁₅ the value by volume of dimes, quarter dollars, and half dollars.

Using the conversion value of 946,353 mm³ in 32 fl. oz., one may calculate the theoretical number of coins that will fit within the target vessel; the fractional portion of the coins has been truncated.

Multiplying the number of coins that will fit in the vessel times the value of each coin, the dollar value of the vessel may be calculated.