$\"\"$

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

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Shell method:

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Vertical axis of revolution.

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The volume of the solid is $\"\"$ .

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The distance from the center of the rectangle to the axis of revolution is $\"\"$ .

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Find the limits of integration by solving point of intersection:

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

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$\"\"$

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$\"\"$ .

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Limits are $\"\"$ .

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The height of the rectangle is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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

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Evaluate $\"\"$ using substitution method.

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Let $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .