$\"\"$

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The curve equation is $\"\"$ .

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The curve is revolved about the $\"\"$ -axis, $\"\"$ .

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Find the limits by equating the equations.

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$\"\"$

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$\"\"$

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Apply zero product rule.

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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The limits are $\"\"$ and $\"\"$ .

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$\"\"$

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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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$\"\"$ .

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The formula for the surface area is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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Power rule of integration: $\"\"$ .

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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 surface area is $\"\"$ .

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$\"\"$

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The surface area is $\"\"$ .