$\"\"$

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

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Find the volume of the region about the $\"\"$ -axis.

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

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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

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Substitute $\"\"$ , $\"\"$ and $\"\"$ 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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Solve for $\"\"$ , when $\"\"$ .

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

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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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$\"\"$ or $\"\"$

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$\"\"$

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$\"\"$ .

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Therefore , the value of $\"\"$ .

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$\"\"$

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The value of $\"\"$ .