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

question 181

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) \(\frac { \pi } { 600 } [ 5 \sqrt { 5 } - 1 ]\)

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