Volumes II
4428 views
|
1
rating
Lesson Summary:
In this lesson, we learn about solids of revolution and how to calculate their volumes using integrals. We see examples of how to find the volume of solids formed by revolving a planar region and discuss how to handle cross-sections that are not disks, but rather, disks with holes called washers. We are also shown how to calculate the volume of a torus using integration.
Lesson Description:
Solids of revolution.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Additional Resources:
- Volume by Parallel Cross Sections; Discs and Washers - Practice with Volume by Parallel Cross Sections; Discs and Washers.
Questions answered by this video:
- What are solids of revolution?
- How do you find volume by revolving a graph around an axis?
- What is the disk method for finding volume?
- How do you find the volume of a solid formed by revolving a region between two graphs?
- What is the washer method for finding volume?
- How do you find the volume of a torus obtained by revolving the unit disk about the line x = 2?
- How do you find volume using the washer method?
- How do you find volume using the disk method?
-
Staff Review
This is a very useful Calculus lesson finding volume by revolving a graph around an axis. The disk method and washer method for finding volume are explained. The animations of the solids are wonderful for understanding exactly what is going on. Some great classic example problems are shown. This is a truly great lesson for understanding volume of solids.
