$\"\"$

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The surface area of the surface by rotating the curve $\"\"$ , about the $\"\"$ -axis is $\"\"$ .

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Rotation about the line $\"\"$ .

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The circle equation is $\"\"$ .

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Solve for $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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For the upper semi circle $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The surface area generated is $\"\"$ .

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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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For the lower semi circle $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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The surface area generated is $\"\"$

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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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The total area is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Apply the formula $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ square units.

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$\"\"$

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$\"\"$ square units.