i.10.5 Flux of the vector field

Calculate the field flux \( \vec{a} \) through the surface \( \mathrm{S} \) using the Gauss-Ostrogradsky formula. \[ \vec{a}=x y \vec{\imath}+y \vec{\jmath}+2 z \vec{k}, \quad \mathrm{~S}:\left\{\begin{array}{l} z=x^{2}+y^{2} \\ z=4, \quad(z \geq 4) \end{array}\right. \]