 # Section 6.2.  Solids of Revolution – if a region in the plane is revolved about a line “line-axis of revolution”  Simplest Solid – right circular cylinder.

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Section 6.2

 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

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

 P.430 # 1-5,15

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

 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.

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.

 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.

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

 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

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

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