Why is the dime smaller than the nickel?
Actually, the first five-cent coin in U.S. history was made of silver and was smaller than today's dime.
That's because when coins were first produced by the U.S. Mint in 1793 the U.S. standard coin was the silver dollar, and additional coin denominations were made with a proportionate silver content to the dollar. This, in turn, established the size of each. For example a ten-cent coin, or dime, contained 1/10 the silver found in a dollar.
The five-cent coin (which contained 1/20 the silver found in a dollar) was eventually determined to be too small to handle, and the five-cent coin we know today as a "nickel" was created in 1866. The size of the coin was increased and its metallic content was changed from silver and copper to a combination of copper and nickel.
—The Fact Monster