A schematic drawing $ofa102-ft$ dome used $by$ a weather service $to$ house radar $is$ shown $to$ the right.

$a.$ How much outside surface $is$ there $to$ paint $(not$ counting the bottom$)?$

$b.$ Express the answer $to$ the nearest square foot.

$a.$ Set $up$ the integral that can $be$ used $to$ find the amount $of$ surface $to$ paint.

$S=$