$\"\"$

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The Parametric equations are $\"\"$ , $\"\"$ , $\"\"$ .

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Surface area:

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If the curve given by the parametric equations $\"\"$ and $\"\"$ , $\"\"$ is rotated about $\"\"$ -axis, then the area of the resulting surface is given by

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$\"\"$ .

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in surface area formula.

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$\"\"$ .

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$\"\"$

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Find integral to determine the area.

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$\"\"$

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$\"\"$

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Let $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Change of integral limits:

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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Substitute corresponding values in the integral.

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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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$\"\"$ .