$\"\"$

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

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The region revolved about the $\"\"$ -axis is $\"\"$ . \ \

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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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Find the integral limits by equating $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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A hole is drilled through this solid, so that one-fourth 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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The removed volume is $\"\"$ .

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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

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The value of $\"\"$ lies on $\"\"$ .

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Therefore, $\"\"$ .

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

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$\"\"$ .

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The diameter of the hole is $\"\"$ .

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$\"\"$

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The diameter of the hole is $\"\"$ .