$\"\"$

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

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The volume of the solid generated revolving about the $\"\"$ - axis.

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Disk method: $\"\"$ .

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Here radius $\"\"$ .

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Integral limits are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Double angle formula: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ cubic units.

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$\"\"$

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Verify the result by using graphing utility.

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Graph the integrand $\"\"$ .

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Find the integral of the function $\"\"$ .

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$\"\"$

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Observe the graph:

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The integral value is $\"\"$ .

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Volume of the region:

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$\"\"$

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Thus, the volume of the region is verified graphically and both the results are almost same.

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$\"\"$

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$\"\"$ cubic units.