# Gauss' Law and enclosed charge

In Halliday and Resnick, I am asked to find the charge on a drum (a cylinder) given the electric field very close to the drum.

In the solutions manual, the author appears to enclose the drum with a Gaussian cylinder in order to find the charge on the drum, but the Gaussian cylinder has the same radius as the drum. Shouldn't the Gaussian cylinder have a radius slightly larger than the drum so that it is enclosed by the Gaussian cylinder? Given that the radius of the Gaussian cylinder need only be 0.00000...1 larger than the drum, is it acceptable to approximate the radius of the Gaussian cylinder as being the same size of the drum's?

Another question related to this is: is the charge on a Gaussian surface enclosed by said Gaussian surface? I know that there are answers to this question on this site, but I could not understand them. Is it even necessary to worry about this in an introductory physics course?