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Calculus I (Assignment Problems) / Applications of Integrals / Volumes of Solids of Revolution / Method of Rings   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Assignment Problems
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Area Between Curves Previous Section   Next Section Volumes of Solids of Revolution/Method of Cylinder

 Volumes of Solids of Revolution / Method of Rings

For problems 1  16 use the method disks/rings to determine the volume of the solid obtained by rotating the region bounded by the given curves about the given axis.

 

1. Rotate the region bounded by ,  and the y-axis about the y-axis.

 

2. Rotate the region bounded by ,  and the y-axis about the x-axis.

 

3. Rotate the region bounded by ,  and the x-axis about the x-axis.

 

4. Rotate the region bounded by ,  and the x-axis about the y-axis.

 

5. Rotate the region bounded by ,  and the x-axis about the x-axis.

 

6. Rotate the region bounded by ,  and the x-axis about the y-axis.

 

7. Rotate the region bounded by ,  and the y-axis about the x-axis.

 

8. Rotate the region bounded by ,  and the y-axis about the y-axis.

 

9. Rotate the region bounded by , , ,  about the y-axis.

 

10. Rotate the region bounded by , , ,  about the x-axis.

 

11. Rotate the region bounded by , ,  and  about the x-axis.

 

12. Rotate the region bounded by  and  about the y-axis.

 

13. Rotate the region bounded by ,  and  about the x-axis.

 

14. Rotate the region bounded by ,  and  about the y-axis.

 

15. Rotate the region bounded by  and  about the x-axis.

 

16. Rotate the region bounded by  and  about the y-axis.

 

17. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by ,  and the y-axis about the

            (a) line                             (b) line  

            (c) line                (d) line   

 

18. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by  and  about the

            (a) line               (b) line  

 

19. Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle with vertices ,  and  about the

            (a) line               (b) line                             (c) line               (d) line                           (e) line                                   (f) line    

 

20. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by , ,  and  about the

            (a) line                             (b) line                             (c) line  

 

21. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by  and  about the

            (a) line               (b) line                             (c) line  

 

22. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by ,  and  about the

            (a) line                             (b) line                            (c) line  

 

23. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by ,  and  about the

            (a) line                             (b) line                             (c) line  

 

24. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by  and  about the

            (a) line                             (b) line               (c) line  

 

25. Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by  and  about the

            (a) line                             (b) line               (c) line  

 

Area Between Curves Previous Section   Next Section Volumes of Solids of Revolution/Method of Cylinder
Integrals Previous Chapter   Next Chapter Extras

Calculus I (Assignment Problems) / Applications of Integrals / Volumes of Solids of Revolution / Method of Rings    [Notes] [Practice Problems] [Assignment Problems]

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