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

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Rotating about the line $\"\"$ .

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Find the volume of the solid using Shell method:

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The surface area of the cylinder is $\"\"$ .

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In this case height of the cylinder is $\"\"$ . radius is $\"\"$ .

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Volume of the solid is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Evaluate the value of $\"\"$ :

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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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Evaluate the value of $\"\"$ :

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$\"\"$

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$\"\"$

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$\"\"$

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Find the value of $\"\"$ .

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Apply reduction formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

\

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Find the limits.

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$\"\"$

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If $\"\"$ ,

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$\"\"$ .

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If $\"\"$ ,

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ cubic units.

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$\"\"$ cubic units.