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Paul
August 7, 2018

Calculus I - Assignment Problems
 Integrals Previous Chapter Next Chapter Extras Area Between Curves Previous Section

## 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 Integrals Previous Chapter Next Chapter Extras

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