Your two lines may disagree. The dime is smaller than the nickel, but it counts for more money. A dime is ten cents. A nickel is five cents. Size and value are different properties.

A denomination is the amount a coin or bill stands for. You cannot find a coin’s denomination just by measuring its width. In this US pair, the smaller coin has the larger denomination.

Try describing the same pair in two ways. "The nickel is bigger" compares size. "The dime is worth more" compares value. Both statements can be true at once. Two nickels count for the same amount as one dime, even though the physical piles look different.

That is the puzzle your drawing uncovered. A bigger circle does not have to mean more money. When you meet an unfamiliar coin, find its value rather than guessing from its size. The next reading follows how these two coins changed over time.

The coins in your comparison have different histories. The US Mint made its first dimes in 1796. Those dimes were small silver coins. Today’s everyday dime is not made of silver.

The five-cent coin changed too. An earlier five-cent coin used silver. In 1866, a new five-cent coin used copper and nickel instead. The name nickel came from its metal. In 1965, silver was removed from the dime.

These changes help us see why a coin’s history matters. The dime and nickel did not begin as two identical pieces of the same material. Yet knowing their materials does not settle every detail of their sizes.

We can be certain about the comparison you made: a dime is smaller and counts for more. We can also follow the documented metal changes. The sources checked here do not explain the exact reason for choosing the nickel’s diameter. Keep that question open rather than turning a possible explanation into a fact.