What is the formula for the volume of a quarter coin?

Answer 1

Coins are not cylinders. The rim of the coin is sometimes raised, as well there are depressions and peaks from the design of the coin. You should use a specific gravity test with water and a scale. bullionultrasound shows how to measure the volume of an American Gold Eagle coin using the specific gravity method, how to calculate density, etc... it's pretty informative.

According to The United states Mint website, a US quarter is 24.26 mm in diameter and the thickness of the coin is 1.75 millimeters.

To find the area of a circle the formula is pi*r^2

so the face of a quarter has an area of pi*(24.26/2)2 = 462.244204 mm2.

To then find the volume we multiple the area of the face by the thickness,

so the volume is 462.244204 * 1.75 or pi * (24.26/2)2 * 1.75= 808.927357mm3.

So the volume of a us quarter is about 808.93 mm3. This does not take into account the ridging on the edge of the coin or the printing on the face.