Question

The outer surface of the cardboard center of a paper towel roll:
is a possible Gaussian surface
cannot be a Gaussian surface because it encloses no charge
cannot be a Gaussian surface since it is an insulator
cannot be a Gaussian surface because it is not a closed surface
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Answer 1

For a Gaussian law suits any closed surface.
In this case with assuming that paper towel roll is not closed surfacethe last option is correct :
cannot be a Gaussian surface because it is not a closed surface