$\"\"$

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A solid is generated by revolving the region bounded by the curve $\"\"$ and $\"\"$ .

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Volume formula: $\"\"$ .

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Here the rotation is about $\"\"$ -axis.

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

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$\"\"$

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

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$\"\"$

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Evaluate $\"\"$ .

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$\"\"$

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$\"\"$

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Volume is $\"\"$ .

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A hole is drilled through this solid, so that one third of the volume is removed.

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Removed volume is $\"\"$ .

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Let $\"\"$ be the radius of the hole.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Diameter of the hole is $\"\"$ .

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$\"\"$

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Diameter of the hole is $\"\"$ .