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### 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

-Doctor Ken,  The Math Forum
```
Associated Topics:
High School Calculus

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