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

Multiple Choice

Find the surface area of the surface S.
- $\mathrm { S }$ is the portion of the surface $10 \sqrt { 7 } x + 10 y ^ { 2 } - 20 \ln y - 30 z = 0$ that lies above the rectangle $0 \leq x \leq 1$ and $1 \leq y \leq 7$ in the $x - y$ plane.

A) $\frac { 2 } { 3 } [ 24 + \ln 7 ]$
B) $\frac { 1 } { 15 } [ 24 + \ln 7 ]$
C) $\frac { 20 } { 3 } [ 24 + \ln 7 ]$
D) $\frac { 4 } { 3 } [ 24 + \ln 7 ]$