Calculate the Area of the Surface S $S$ Is the Cap Cut from the Paraboloid

Multiple Choice

Calculate the area of the surface S.
- $S$ is the cap cut from the paraboloid $z = \frac { 2 } { 5 } - 10 x ^ { 2 } - 10 y ^ { 2 }$ by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ .

A) $\frac { \pi } { 300 } [ 65 \sqrt { 65 } - 1 ]$
B) $\frac { 1 } { 600 } [ 5 \sqrt { 5 } + 1 ]$
C) $\frac { \pi } { 300 } [ 5 \sqrt { 5 } - 1 ]$
D) $\frac { \pi } { 600 } [ 5 \sqrt { 5 } - 1 ]$