Find the Surface Area of the Surface S $\mathrm { S }$

Multiple Choice

Find the surface area of the surface S.
- $\mathrm { S }$ is the paraboloid $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } - \mathrm { z } = 0$ below the plane $\mathrm { z } = 2$ .

A) $\frac { 13 } { 6 } \pi$
B) $\frac { 9 } { 2 } \pi$
C) $\frac { 13 } { 3 } \pi$
D) $\frac { 13 } { 2 } \pi$