1/23/2012
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Math 104 – Rimmer
6.2 Volumes by Cylindrical Shells
Sometimes finding the volume of a solid of revolution is
impossible
by the disk or washer method
(
)
2
sin
y
x
=
π
Since there is a gap b/w the region and the axis
of rotation, we would try washer method
We would have to solve for
as a function of
since the axis of rotation is vertical.
Sometimes this is the problem, but we can do it here.
x
y
1
sin
x
y

=
Our problem is that the outer radius and the inner
radius use the
.
same curve
In order to find the volume of this solid of revolution we need a
different technique.
6.2 Volumes by Cylindrical Shells
Math 104 – Rimmer
6.2 Volumes by Cylindrical Shells
The
Method of Cylindrical Shells
uses the volume of
nested
cylinders
to find the volume of a solid of revolution.
To understand the formula, lets first look at one of the cylindrical shells:
There are two cylinders, an outer cylinder
and an inner cylinder.