What is very interesting is that a 10 cent coin is the smallest in other currencies as well. For example Canada's 10 cents, or UK 10 pence ( or sixpence back in the day). Also, old Soviet 10 kopek coin was the smallest, even though there were 1, 2, 3, 5 kopek coins which were larger in size. What is so different about 10 cents?
The value of coins originated with the metals they were made of, so a coin's size, composition, and value were all related to each other.
In the Canadian case, dimes were originally made of silver and didn't need to be large to be worth ten cents. Like many silver coins, they had grooves on the edge to keep people from shaving silver off of them.
Five-cent coins were originally also made of silver, and were even smaller than dimes (exactly half by weight). In 1922, Canadian five-cent coins switched from silver to nickel, got much larger, and became known as nickels.
Canadian pennies were originally made of copper, so they were naturally larger than dimes despite being one-tenth the value.
It's essentially due to the silver standard - here's an old reddit TIL post on it.
As for why the nickel is so large and thus outside the silver standard - not sure. The old Buffalo Nickels were silver, and perhaps that just points to how much the real value of silver had deflated(inflated? though the currency is deflating?) between the advent of 5 cents of silver to when they standardized the value of 10 cents of silver. It might be a left over from the 1880s when western silver miners had an abundance of supplies and pushed for including silver within the US gold standard. Someone else surely knows more about this than me.