Volumes of Solids of Revolution / Method of Rings. In this section we will start looking at the volume of a solid of revolution. We should first define just what a solid of revolution is. To get a solid of revolution we start out with a function, ;" /> ;" />. on an interval [ a,b ]. We then rotate this curve about a given axis to get the surface of the solid of revolution. For purposes of this discussion let’s rotate the curve about the x -axis, although it could be any vertical or horizontal axis.
Doing this for the curve above gives the following three dimensional region. What we want to do over the course of the next two sections is to determine the volume of this object. In the final the Area and Volume Formulas section of the Extras chapter we derived the following formulas for the volume of this solid.
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