i.10.4 Flux of the vector field

Calculate the field flux \( \vec{a} \) through the closed surface S using the Ostrogradsky-Gauss formula. \[ \vec{a}=x y \vec{\imath}+y \vec{\jmath}+2 \vec{k}, \quad \mathrm{~S}:\left\{\begin{array}{lr} x^{2}+y^{2}+z^{2}=16 \\ z=1, \quad(z \geq 1) \end{array} .\right. \]