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

2. Section 7.3b

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… x f(x) Cross section area: Integrate to find volume:

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. x f(x) Cross section area: Volume: y = sin(x)cos(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. x f(x) y = sin(x)cos(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. y f(y) Cross section area: Volume: y = 2 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. x f(x) Cross section area: Volume: x = 2

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: Volume: x = 1 x f(x)