Find the Surface Area of the Surface S $S$ Is the Cap Cut from the Sphere

Multiple Choice

Find the surface area of the surface S.
- $S$ is the cap cut from the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ by the cone $z = 6 \sqrt { x ^ { 2 } + y ^ { 2 } }$ .

A) $16 \left( 1 - \frac { 6 \sqrt { 37 } } { 37 } \right)$
B) $16 \left( 1 - \frac { 6 \sqrt { 37 } } { 37 } \right) \pi$
C) $32 \left( 1 - \frac { 6 \sqrt { 37 } } { 37 } \right) \pi$
D) $16 \left( \frac { 6 \sqrt { 37 } } { 37 } - 1 \right) \pi$