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

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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 Cylinder Previous Section   Next Section Work

 

1. Find the volume of a pyramid of height h whose base is an equilateral triangle of length L. [Solution]

 

2. Find the volume of the solid whose base is a disk of radius r and whose cross-sections are squares.  See figure below to see a sketch of the cross-sections.

 

[Solution]

 

3. Find the volume of the solid whose base is the region bounded by  and  and whose cross-sections are isosceles triangles with the base perpendicular to the y-axis and the angle between the base and the two sides of equal length is .  See figure below to see a sketch of the cross-sections.

 

[Solution]

 

4. Find the volume of a wedge cut out of a “cylinder” whose base is the region bounded by ,  and the x-axis.  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  they are just in a different orientation).

 

[Solution]

 

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

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

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