Calculate the Area of the Surface S $S$ Is the Portion of the Cone

Calculate the area of the surface S.
- $S$ is the portion of the cone $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 9 } = \frac { z ^ { 2 } } { 25 }$ that lies between $z = 4$ and $z = 5$ .

A) $\frac { 27 } { 25 } \sqrt { 34 } \pi$
B) $\frac { 123 } { 25 } \sqrt { 34 } \pi$
C) $\frac { 123 } { 25 } \sqrt { 34 }$
D) $\frac { 81 } { 25 } \sqrt { 34 } \pi$