Calculate the Area of the Surface S $S$ Is the Lower Portion of the Sphere

Multiple Choice

Calculate the area of the surface S.
- $S$ is the lower portion of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 49$ cut by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ .

A) $49 \left( \frac { \sqrt { 2 } } { 2 } + 1 \right)$
B) $14 \left( \frac { \sqrt { 2 } } { 2 } + 1 \right) \pi$
C) $98 \left( \frac { \sqrt { 2 } } { 2 } + 1 \right) \pi$
D) $49 \left( \frac { \sqrt { 2 } } { 2 } + 1 \right) \pi$