4.8 Volumes of Solids of Revolution

 

Summary

Integrals find application in many modeling situations involving continuous variables such as area. They allow us to model physical entities that can be described through a process of adding up, or accumulating, smaller infinitesimal parts. In this section, the Riemann Sum approach is used to develop an integral formula for the volume of a solid of revolution.

By the end of your studying, you should know:

On-screen applet instructions: The applet depicts approximating the volume of a solid of revolution with a finite number n of disks. Use the pull-down menu to change the value of n.

Examples

Find the volume of the solid generated by rotating the region R bounded by the y axis, the line y = a, and the curve

Find the volume of the solid generated by rotating the region bounded by y = x, y = 3 – x, and x = 4 around the line x = 5.

Find the volume of the torus of radius a with inside radius b.

Applets

Volume By Disks

Volume By Shells

Videos

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Quiz

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Exercises

See Exercises for 4.8 Volumes of Solids of Revolution (PDF).

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4.7 Areas Between Curves Table of Contents 4.9 Arc Length


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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel