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

Calculate the area of the surface S.
- $S$ is the portion of the paraboloid $z = 3 x ^ { 2 } + 3 y ^ { 2 }$ that lies between $z = 4$ and $z = 5$ .

A) $\frac { \pi } { 9 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]$
B) $\frac { 1 } { 27 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]$
C) $\frac { \pi } { 54 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]$
D) $\frac { \pi } { 27 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]$