1. Solids not generated by Revolution
Volumes of Solids
Solids
Solids of Revolution
Solids not generated by Revolution
Examples: Classify the solids

2. Solids not generated by Revolution
Volumes of Solids
Solids
Solids of Revolution
Solids not generated by Revolution

3. Solids not generated by Revolution
Volumes of Solids
Solids
Solids of Revolution
Solids not generated by Revolution
Cross-Sections
Sec(6.2)
Volumes Using Cross-Sections
Volumes Using Cylindrical Shells
Sec(6.2)
Sec(6.3)
The Disk
Method
The Washer
Method

4. Solids of Revolution Volumes of Solids
Solids of Revolution needs visualization skills
The following slides provide better opportunities to improve such skills.
Solids of Revolution
Volumes Using Cross-Sections
Volumes Using Cylindrical Shells
Sec(6.1)
Sec(6.2)
The Disk
Method
The Washer
Method

5. Visualize it in your mind
Solids of Revolution
rotate the red line about the x-axis
Visualize it in your mind

6. Visualize it in your mind
Solids of Revolution
solid obtained by rotating a region
Visualize it in your mind
What is the shape of a solid if you rotate the Square about the y-axis
What is the shape of a solid if you rotate the triangle about the y-axis

7. Solids of Revolution

8. Solids of Revolution

9. Solids of Revolution

10. Solids of Revolution

11. Solids of Revolution

12. solid obtained by rotating a region
VOLUMES
solid obtained by rotating a region
use your imagination