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

Multiple Choice

Find the surface area of the surface S.
- $S$ is the paraboloid $x ^ { 2 } + y ^ { 2 } - z = 0$ between the planes $z = 0$ and $z = 6$ .

A) $\frac { 124 } { 3 } \pi$
B) $\frac { 31 } { 3 } \pi$
C) $\frac { 62 } { 3 } \pi$
D) $31 \pi$