i.10.i Flux of the vector field

Calculate the vector field flux \( \vec{a} \) through the lateral surface of the cone directly and using the Gauss-Ostrogradsky formula: \[ \vec{a}=x \vec{\imath}+y \vec{\jmath}+z \vec{k}, \quad S:\left\{\begin{array}{l} z=1-\sqrt{x^{2}+y^{2}} \\ z \geq 0, \quad z \leq 1 \end{array} .\right. \]