Final answer:
Given that electric field lines enter a box-shaped volume with no charges inside, and based on Gauss's Law, the same number of electric field lines must exit the box, which would be 11 lines.
Step-by-step explanation:
The question pertains to the concepts of electric field lines and electric flux as described by Gauss's Law. According to this law, the net electric flux through a closed surface is proportional to the charge enclosed within the surface. In the scenario where there are no charges within the enclosed surface, the net electric flux must be zero. This means that every electric field line that enters the box must also exit it because electric field lines originate from positive charges and terminate at negative charges or at infinity if the charges are isolated. Since the question states that 11 electric field lines enter the box and there are no charges inside to terminate those lines, all 11 lines must also exit the box.