Toilet Paper Mysteries
Pyth, 27 23 bytes

+fg0=-QJc*.n0+18T50)cQJ


Try it online. Test suite.


Explanation

                            Q = input number (implicit)
 f                 )        increment T from 1, for each T:
             +18T             add 18 to T, get radius
         *.n0                 multiply by pi to, get half the circumference
        c        50           divide by 50, get circumference in sheets
       J                      save it to J
    =-Q                       decrement Q by it
  g0                          use this T if Q is now &lt;= 0
+                           add
                     Q        Q (now &lt;= 0)
                    c J       divided by J (the last circumference)
                            and print (implicit)