Let S be the parametric surface defined by r$($u$,$v$)=(3$sin$($u$)$cos$($v$),3$sin$($u$)$sin$($v$),3$cos$($u$)),$ where $($u$,$v$)$ has a

domain of $[0,(\backslash$pi $)/(2)]\backslash$times $[0,2\backslash$pi $].$

$($a$)$ Surface S defines the top half of a sphere of radius three centered at the origin. It's boundary C is the closed

parametric curve r$($t$)=(3$cos$($t$),3$sin$($t$),0),$ where t