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.