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

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On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

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Paul
August 7, 2018


Calculus I - Practice Problems
Integrals Previous Chapter   Next Chapter Extras
Volumes of Solids of Revolution / Method of Rings Previous Section   Next Section More Volume Problems

For problems 1  8 use the method of 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 , the x-axis and the y-axis about the x-axis. [Solution]

 

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

 

3. Rotate the region bounded by  and  about the y-axis.  For this problem assume that . [Solution]

 

4. Rotate the region bounded by  and  about the x-axis.  For this problem assume that . [Solution]

 

5. Rotate the region bounded by ,  and  about the line . [Solution]

 

6. Rotate the region bounded by  and  about the line . [Solution]

 

7. Rotate the region bounded by  and  about the line . [Solution]

 

8. Rotate the region bounded by , ,  and  about the line . [Solution]

 

Problem Pane
Volumes of Solids of Revolution / Method of Rings Previous Section   Next Section More Volume Problems
Integrals Previous Chapter   Next Chapter Extras

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

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