When to use the Shell Method or Washer Method to Calculate Volume

Date: 2/26/96 at 20:10:5
From: Anonymous
Subject: calculus help

I'm taking AB Calculus and we are learning about applications of 
definite integrals.  We recently learned about the washer method 
and shell method.  However, I was wondering which method to use in 
different situations. 

Thanks a lot. 

T.J.
Pascalides@aol.com 

Date: 2/27/96 at 13:24:24
From: Doctor Ken
Subject: Re: calculus help

Hello!

Well, to tell the truth, it just depends on whichever method is 
easiest.Sometimes you'll be able to do both with about the same 
ease, for example find the volume of the object formed when the 
triangle with vertices (0,0), (1,0), and (1,1) is revolved around 
the y-axis.

Sometimes it just doesn't make sense to do it one way or the 
other, though.  For instance, find the volume of the object formed 
when a piece (from 0 to 5Pi, for instance) of the Sine curve is 
revolved around the x-axis.  It would be pretty silly to use the 
shell method, because then you'd have to try to take horizontal 
area slices between the Sine curve and the x-axis.  So the washer 
method is pretty much the way to go on this one.

But in general, you just kind of have to look at the problem and 
decide whether horizontal slices or vertical slices are easier to 
work with for your function.

-Doctor Ken,  The Math Forum