Lecture 24 : Volume of solids of revolution by washer method [Section 24.1]
24.1.4
Note:
For a solid of revolution the slice is taken in planes perpendicular to the axis of revolution. For example, if a plane region between the two curves given by functions
is revolved around , then the slice of thickness by a plane perpendicular to at a point is a circular washer of inner radius and of outer radius . Thus, its cross sectional area is ,
and the volume of the corresponding solid of revolution is given by
24.1.5
Examples:
(i)
Consider a solid obtained by revolving about the the triangular region in the first quadrant bounded by
between the two curves given by functions 
, then the slice of thickness 
by a plane perpendicular to 
at a point 
is a circular washer of inner radius 
and of outer radius 
. Thus, its cross sectional area is 
, 
the triangular region in the first quadrant bounded by 
. 
