Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 9, x = 0, y = 9, y = 11
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Step-by-step explanation:
The Volume of a representative shell is
2
π
r
h
thickness
Since the thickness is
d
x
(the variable we will work with is
x
) we note that
x
varies from
−
2
to
2
.
The radius of the shell is
r
=
2
−
x
.
The height is the upper curve minus the lower curve
h
=
(
8
−
x
2
)
−
(
x
2
)
=
8
−
2
x
2
So the volume of the solid of revolution is
V
=
∫
2
−
2
2
π
(
2
−
x
)
r
(
8
−
2
x
2
)
h
thickness
d
x
=
2
π
[
128
3
]
=
256
π
3
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