Volumes I
In this lesson on Volumes I, we learn how to calculate the volumes of various solids with specified cross-sections by integrating the cross-sectional area. We see how to approximate the volume with layers of cross-sectional area times thickness and how this approximation converges to the exact volume as delta x approaches zero. The lesson provides examples of finding the volume of solids with square, parabolic, and semicircular cross-sections. Finally, we derive the formula for the volume of a right circular cone with height H and radius R.
Solids with specified cross-sections.
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.
- Volume by Parallel Cross Sections; Discs and Washers - Practice with Volume by Parallel Cross Sections; Discs and Washers.
- How do you find the volume of a solid with cross-sectional area?
- How do you find the volume of a solid using integrals?
- How do you find the volume of a solid whose base is bounded by y = 1 - x^2?
- What is the volume differential?
- How can you derive the formula of a right circular cone using integrals?
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Staff Review
This video is about the integration of cross-sectional area. Parts of this video are rather theoretical, although the images are really impressive and helpful. Some example problems of finding the volume of solids are shown. Some cross-sections are squares, while in other examples the cross-sections are semi-circles. This is a very useful and interesting video.
