The maximum amount of dimes that can fit into one gallon is 11,159 based on the volume of a dime and the volume of a gallon in cubic inches. This calculation assumes each dime fits into the gallon perfectly, with a minimum amount of air in the container.
A dime is 0.705 inch in diameter, with a radius of 0.3525 inch, and a thickness of 0.053 inch. The volume of a cylinder is the radius squared times pi times the thickness, which means one dime takes up approximately 0.0207 cubic inch of space.
A U.S. gallon is 231 cubic inches. Divide 231 cubic inches per gallon by 0.0207 cubic inch per dime to get a maximum of 11,159 dimes per gallon.