I.10.15 Flux of the vector field

condition: Find the flow of the vector \( a=i y^{2}+j x^{2}+k z^{2} \) through the part of the outer side of the cylinder \( x^{2}+y^{2}=a^{2} \), located in the first octant between the planes \( z=0, z=a \), \( a>0 \).