$\"\"$

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(a)

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The curve is $\"\"$ , where $\"\"$ .

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$\"\"$

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The differential of arc length : $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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

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$\"\"$

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$\"\"$

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Surface area of the curve when rotated about $\"\"$ -axis : $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above formula.

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$\"\"$

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$\"\"$

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$\"\"$

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The surface area of the curve rotated about $\"\"$ -axis is $\"\"$ .

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$\"\"$

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(b)

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Surface area of the curve when rotated about $\"\"$ -axis : $\"\"$ .

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Substitute $\"\"$ in the above formula.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The surface area of the curve rotated about $\"\"$ -axis is $\"\"$ .

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$\"\"$

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(a) The surface area of the curve rotated about $\"\"$ -axis is $\"\"$ .

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(b) The surface area of the curve rotated about $\"\"$ -axis is $\"\"$ .