Module 8 : Applications of Integration - II
Lecture 24 : Volume of solids of revolution by Shell method [Section 24.2]
(ii)
 A notable difference between the Washer Method and the Shell Method is that in the former we take slices
  perpendicular to the axis of revolution while in the latter we take slices parallel to the axis of revolution.
(iii)

Let be the region between the two curves given by Riemann integrable functions

 

             
Suppose and the region is revolved about the -axis, then analogous to equation (15), the volume of this solid of revolution is given by
            .
24.2.3 Examples
(i)

A solid cone of height and radius is obtained by revolving about the -axis the triangular region bounded

 

by the lines
           
 
 

Thus, the Shell Method its volume is given by
            
1
10