$\"\"$

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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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Consider the function $\"\"$ .

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Graph:

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Graph the function $\"\"$ .

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$\"\"$

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Observe the graph:

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$

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$\"\"$

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$\"\"$ .

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Therefore, the option $\"\"$ is the correct choice.

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$\"\"$

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The option $\"\"$ is the correct choice.