How many dimes make 1 oz of silver?

Presuming that you are referring to US dimes issued between 1875 and 1964 (dimes older than 1875 had different weights and/or fineness), dimes weigh 2.50 grams and are 90% silver (the remaining 10% is copper). This means that the ASW (Actual Silver Weight) is 0.07234 troy ounces. Thus, it would require 14 dimes (this number is rounded up; the precise number is 13.8236 dimes) to have one troy ounce of silver.