$\"\"$

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The equations are $\"\"$ and $\"\"$ on $\"\"$ .

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If the curve given by the parametric equations $\"\"$ and $\"\"$ on $\"\"$ is rotated about the $\"\"$ -axis, where $\"\"$ are continuous and $\"\"$ , then the surface area is $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Surface area is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply parts of integration formula: $\"\"$ .

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Consider $\"\"$ .

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .