How many dollars are in a gallon of quarters?

Answer 1

There is no possible way to answer the question because quarters are circular. This means that they leave gaps between them whatever the shape of the container - except in one special case. The diameter of a quarter is 0.955 inches - lets say 1 inch for simplicity. Then, a circular container with a diameter of 3 inches will hold seven coins in one layer, implying a waste of 22.22% of the space. The diameter of the container can be increased to 3.05 inches without increasing the number of coins which will fit, so that the proportion of wasted space increases to more than a quarter.

The one exceptional shape is if the container is in the shape of a long tube whose diameter is the same as the diameter of a quarter. This will give a single stack of quarters with no wasted space. Such a stack will contain approx 17,248 quarters which equals 4,312 dollars. However, other than in this special case, the amount will be substantially smaller because of wasted space.