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

Calculus I - Assignment Problems
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Volumes of Solids of Revolution / Method of Rings Previous Section   Next Section More Volume Problems

 Volumes of Solids of Revolution / Method of Cylinders

For problems 1  8 use the method cylinders 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 ,  and  about the y-axis.

 

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

 

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

 

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

 

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

 

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

 

15. Use the method of cylinders 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   

 

16. Use the method of cylinders to determine the volume of the solid obtained by rotating the region bounded by ,  and the x-axis about the

            (a) line               (b) line  

            (c) line                             (d) line   

 

17. Use the method of cylinders to determine the volume of the solid obtained by rotating the region bounded by  and  about the

            (a) line                            (b) line  

 

18. Use the method of cylinders 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    

 

19. Use the method of cylinders to determine the volume of the solid obtained by rotating the region bounded by , ,  and  about the

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

 

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

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

 

Volumes of Solids of Revolution / Method of Rings Previous Section   Next Section More Volume Problems
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Calculus I (Assignment Problems) / Applications of Integrals / Volumes of Solids of Revolution/Method of Cylinder    [Notes] [Practice Problems] [Assignment Problems]

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