Option C
The outer surface of the cardboard center of a paper towel roll: cannot be a Gaussian surface because it is not a closed surface.
A Gaussian surface is a bounded surface, ie. an impounded plain, bounded by space which can be practiced in obtaining out the mass of flux of electric, gravitational, or any additional field.
It should be closed surface so that a precise estimation can be performed within points that are inside the cover, on the surface, and outside the cover is the prime part of this. In this problem with considering that paper towel roll is not a closed surface, it is not a gaussian surface.