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Section 6.2

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Solids of Revolution – if a region in the plane is revolved about a line “line-axis of revolution” Simplest Solid – right circular cylinder or “Disc” Volume: circular cylinder = πr 2 h

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Disc Method – representative rectangle is perpendicular to axis (and touches axis of rotation) i) Horizontal Axis of Revolution i) Vertical Axis of Revolution

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P.430 # 1-5,15

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Representative rectangle is perpendicular to the axis of revolution (does NOT touch the axis) Solid of Revolution with a hole

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Outer radius – inner radius

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Find the volume of the solid generated by revolving the region bounded by the graph of y=x 3, y=1, and x=2 about the x-axis.

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Find the volume of the solid generated by revolving the region bounded by the graph of y=x 3, y=x, and between x=0 and x=1, about the y-axis.

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Find the volume of the solid formed by revolving the region bounded by the graphs y=4x 2 and y=16 about the line y=16.

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Find the volume of the solid formed by revolving the region bounded by the graphs y=2 and about the line y=1.

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Find the volume of the solid formed by revolving the region bounded by the graphs y=0, x=1 and x=4 about the line y=4

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P.430 # 11, 16, 17, 19, 23, 27, 32, 34

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