1. 7.2 Volume: The Disk Method (Day 3) (Volume of Solids with known Cross- Sections) Objectives: -Students will find the volume of a solid of revolution using the disk method -Students will find the volume of a solid of revolution using the washer method -Students will find the volume of a solid with known cross sections

2. Volume of Solid Formed -cross sections ⊥ to x-axis -cross sections ⊥ to y-axis Sums up all Cross-sections Area formula – depends on what type of cross-section

3. Ex 1) Find the volume of the solid whose base is bounded by with the indicated cross-sections taken ⊥ to the x-axis base of cross-sections f(x) g(x)

4. Ex 1) base of cross-sections: a) squares: f(x) g(x) 2 – x

5. Ex 1) base of cross-sections: b) equilateral triangles: f(x) g(x) 2 – x

6. Ex 1) base of cross-sections: c) semicircles: f(x) g(x) 2 – x

7. Ex 1) base of cross-sections: d) isosceles right triangle: f(x) g(x) 2 – x

8. Note on semiellipses: Area of whole ellipse: Area of semiellipse: b a

9. Find the volume of the figure enclosed by the graphs of and. Use cross-sections of semi-circles that are perpendicular to the y-axis. Base: Area of cross-sections: Volume:

10. Find the volume when has square cross-sections that are perpendicular to the x-axis. Base: Area of cross-sections: Volume: