The rubber ball, in this case, can be considered a circle with a circumference of 13 inches. So, we can find the diameter of the rubber ball using the formula 
or 
. That is
Therefore, the diameter is greater than 4 inches and less than 5 inches. That means the smallest box that the ball will fit into with the top on is the 5 inches box.
Therefore, the diameter is greater than 4 inches and less than 5 inches. That means the smallest box that the ball will fit into with the top on is the 5 inches box.