Let $S_{1}be$ the surface $of$ the cone $z=\sqrt[\phantom{2}]{x^2+y^2},0z1,$ and let $S_{2}be$ the round "lid" $at$ the

top $of{S}_1.$ Let $S=S_1{S}_2,so$ that $Sis$ a closed surface. Orient $Sso$ that its normal vectors

are $in$ the outward direction.

$(a)$ Find a parametrisation $Tof{S}_1$ and write down its normal vector.

$(b)$ Let $Fbe$ the vector field $F(x,y,z)=(y,0,z).$ Compute the flux

${}_{S}F*hat(n)dS$

where hat$(n)is$ the outward normal $to$ the surface $S$

$(Please$ show full working and explanation $to$ understand$)$