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Calculus I (Assignment Problems) / Applications of Integrals / More Volume Problems   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Assignment Problems
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 More Volume Problems

 

1. Use the method of finding volume from this section to determine the volume of a sphere of radius r.

 

2. Find the volume of the solid whose base is the region bounded by  and  and whose cross-sections are squares with the base perpendicular to the y-axis.  See figure below to see a sketch of the cross-sections.

 

 

 

3. Find the volume of the solid whose base is a disk of radius r and whose cross-sections are rectangles whose height is half the length of the base and whose base is perpendicular to the x-axis.  See figure below to see a sketch of the cross-sections (the positive x-axis and positive y-axis are shown in the sketch).

 

 

 

4. Find the volume of the solid whose base is the region bounded by  and  and whose cross-sections are equilateral triangles with the base perpendicular to the y-axis.  See figure below to see a sketch of the cross-sections.

 

5. Find the volume of the solid whose base is the region bounded by  and  and whose cross-sections are the upper half of the circle centered on the y-axis.  See figure below to see a sketch of the cross-sections.

 

 

 

6. Find the volume of a wedge cut out of a “cylinder” whose base is the region bounded by  and the x-axis between .  The angle between the top and bottom of the wedge is .  See the figure below for a sketch of the “cylinder” and the wedge (the positive x-axis and positive y-axis are shown in the sketch).

 

 

 

7. For a sphere of radius r find the volume of the cap which is defined by the angle  where  is the angle formed by the y-axis and the line from the origin to the bottom of the cap.  See the figure below for an illustration of the angle .

 

 

Volumes of Solids of Revolution/Method of Cylinder Previous Section   Next Section Work
Integrals Previous Chapter   Next Chapter Extras

Calculus I (Assignment Problems) / Applications of Integrals / More Volume Problems    [Notes] [Practice Problems] [Assignment Problems]

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