$\"\"$

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

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(a)

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(1) Draw the coordinate plane.

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(2) Graph the functions $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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When we rotate a thin horizontal strip as shown in the figure about the $\"\"$ axis, we get a disc with radius $\"\"$ .

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The width of the disc is $\"\"$ .

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

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Find volume integrate $\"\"$ to $\"\"$ .

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Substitute the values in the equation.

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$\"\"$

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Apply integration :

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$\"\"$

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$\"\"$

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(b)

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(1) Draw the coordinate plane.

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(2) Graph the functions $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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When we rotate a thin horizontal strip as shown in the figure about the $\"\"$ axis, we get a washer

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with inner radius $\"\"$ and outer radius $\"\"$ .

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$\"\"$

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Squaring on both sides.

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$\"\"$ .

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The width of the washer is $\"\"$ .

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Volume of the washer is $\"\"$ .

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$\"\"$

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Find volume integrate $\"\"$ to $\"\"$ .

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$\"\"$ .

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Apply integration:

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$\"\"$

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$\"\"$

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(C)

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(1) Draw the coordinate plane.

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(2) Graph the functions $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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When we rotate a thin horizontal strip as shown in the figure about the line $\"\"$ , we get a radius $\"\"$ .

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$\"\"$

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Squaring on both sides.

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$\"\"$ .

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The width of the disc is $\"\"$ .

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Volume of the disc is $\"\"$ .

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$\"\"$

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Find volume integrate $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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(d)

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(1) Draw the coordinate plane.

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(2) Graph the functions $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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When we rotate a thin horizontal strip as shown in the figure about the line $\"\"$ we get a washer with inner radius $\"\"$ and outer radius $\"\"$ .

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$\"\"$

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Squaring on both sides.

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$\"\"$ .

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The width of the disc is $\"\"$ .

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Volume of the washer is $\"\"$ .

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$\"\"$

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Find volume integrate $\"\"$ to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .

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(d) $\"\"$ .