Volumes of Revolution Cross Sections

byubound
Wed, 28 Apr 2010 23:24:31 +0000

These questions sometimes appear as one of the parts on a free response for area/volume problems. The pattern seems to be that you find the area of the region in the first part of the free response and then one of the other parts of the problem is to find the volume with a known cross section. You have to use the area that you find in the first part in the integral you use in the cross section part of the question. In order to find the volume with the known cross section, it depends on what type of cross section the problem is asking for. If the problem states that the known cross section is:

A square - you take the integral of the following: ( base^2 )

An equilateral triangle - you take the integral of the following: ( base^2 * (√3)/4 )

A semicircle - you take the integral of the following: ( radius^2 * pi/8 )

Make sure when you take the integral that the bounds are the same as the bounds for the area you found in the first part of the problem. I hope this helps.