QUESTION $4$

$(a)$ Given that vector field $F=($:$x,3,z-y$:$)$ and $Gbe$ the solid cone enclosed $by$ surface $S$ that consists $ofz=\sqrt[\phantom{2}]{x^2+y^2},$ with the circular top from $z2.$ Use the Divergence Theorem $to$ evaluate ${}_G$grad$*FdV.$

$(b)$ Use Stoke's Theorem $to$ evaluate

${}_{C}F*dr$

$ifF=2zi+3xj+5yk$ and the boundary $of$ the portion $of$ the paraboloid for which $z0.Cis$ the interaction $of$ the paraboloid, $z=4-x^2-y^2$ and $xy$ plane with a counterclockwise orientation looking down $at$ the $z-$axis.