Find the Surface Area of the Surface S $S$ Is the Portion of the Paraboloid

Multiple Choice

Find the surface area of the surface S.
- $S$ is the portion of the paraboloid $z = 81 - x ^ { 2 } - y ^ { 2 }$ that lies above the ring $16 \leq x ^ { 2 } + y ^ { 2 } \leq 36$ in the $x y$ -plane.

A) $\frac { \pi } { 4 } [ 145 \sqrt { 145 } - 65 \sqrt { 65 } ]$
B) $\frac { \pi } { 2 } [ 145 \sqrt { 145 } - 65 \sqrt { 65 } ]$
C) $\frac { \pi } { 6 } [ 145 \sqrt { 145 } - 65 \sqrt { 65 } ]$
D) $\frac { \pi } { 3 } [ 145 \sqrt { 145 } - 65 \sqrt { 65 } ]$