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

Multiple Choice

Calculate the area of the surface S.
- $S$ is the portion of the plane $7 x + 8 y + 7 z = 4$ that lies within the cylinder $x ^ { 2 } + y ^ { 2 } = 1$ .

A) $\frac { 1 } { 7 } \pi$
B) $\frac { 18 } { 7 } \sqrt { 2 } \pi$
C) $\frac { 9 } { 7 } \sqrt { 2 } \pi$
D) $\frac { 9 } { 7 } \sqrt { 2 }$