Hi$!$ Please please, evaluate step by step. The answer is $27$ pi$,$ i am just notunderstanding the steps to get there. Thank you! This will really help for my final!

Let $S$ be the closed surface which is the portion of the sphere $x^2+y^2+z^2=4$ with $-2z1$ topped by the disk in the plane $z=1,$ oriented outward. Then the flux of vec$(r)=$xvec$(i)+$yvec$(j)+$zvec$(k)$ through $S$ is:

Let $S$ be a circular cylinder of radius $0\mathrm{.}2,$ such that the center of one end is at the origin and the cent