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Exploring 3D Volumes: Techniques for Computing Solids in Three Dimensions

Learn about computing volumes of solids in three dimensions with techniques such as limits of Riemann sums, cross sections, and solids of revolution using washers or cylindrical shells.

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Exploring 3D Volumes: Techniques for Computing Solids in Three Dimensions

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  1. Volumes Chapter 8 Applications of Definite Integral Section 8.3

  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

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