1. Chapter 8
Applications of Definite Integral
Section 8.3
Volumes

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about
Volumes as limits of Riemann sums
Volumes with circular, square, or other cross sections
Volumes of solids of revolution using washers or cylindrical shells
…and why
The techniques of this section allow us to compute
volumes of certain solids in three dimensions.

5. Volume of a Solid

6. How to Find Volumes by the Method of Slicing

7. Example Square Cross Sections

8. Example Square Cross Sections

9. Example A Solid of Revolution

10. Example Finding Volumes Using Cylindrical Shells

11. Example Finding Volumes Using Cylindrical Shells

12. Example Finding Volumes Using Cylindrical Shells

13. Example Finding Volumes Using Cylindrical Shells

14. Example Other Cross Sections

15. Example Other Cross Sections

16. Quick Quiz Sections 8.1 – 8.3

17. Quick Quiz Sections 8.1 – 8.3

18. Quick Quiz Sections 8.1 – 8.3

19. Quick Quiz Sections 8.1 – 8.3

20. Quick Quiz Sections 8.1 – 8.3

21. Quick Quiz Sections 8.1 – 8.3