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Do Now: #10 on p.391

Do Now: #10 on p.391. Cross section width:. Cross section area:. Volume:. Section 7.3b. Solids of revolution. Solid of Revolution – solid with circular cross sections (usually obtained by rotating a function or functions about a particular axis). Ex: The region between the graph of

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Do Now: #10 on p.391

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  1. Do Now: #10 on p.391 Cross section width: Cross section area: Volume:

  2. Section 7.3b Solids of revolution

  3. Solid of Revolution – solid with circular cross sections (usually obtained by rotating a function or functions about a particular axis) Ex: The region between the graph of and the x-axis over the interval [–2, 2] is revolved about the x-axis to generate a solid. Find the volume of this solid. Graph the function… and visualize the solid… Cross section area: f(x) Integrate to find volume: x

  4. More Guided Practice Find the volume of the solid generated when the region in the first quadrant under the curve y = sin(x)cos(x) is revolved about the x-axis. Cross section area: y = sin(x)cos(x) f(x) Volume: x

  5. More Guided Practice Find the volume of the solid generated when the region in the first quadrant under the curve y = sin(x)cos(x) is revolved about the x-axis. y = sin(x)cos(x) f(x) x

  6. More Guided Practice Find the volume of the solid generated when the region in the first quadrant above the line x = 3y/2 and below the line y = 2 is revolved about the y-axis. Cross section area: y = 2 f(y) y Volume: Right circular cone of radius 3 and height 2:

  7. More Guided Practice Find the volume of the solid generated when the region bounded by the cubing function and the lines y = 0 and x = 2 is revolved about the x-axis. Cross section area: x = 2 Volume: x f(x)

  8. More Guided Practice Find the volume of the solid generated when the region bounded by the function and the line y = 0 is revolved about the x-axis. Cross section area: x = 1 x Volume: f(x)

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