Volumes_Using_Cylindrical_Shells.ppt

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VOLUMES BY CYLINDRICAL SHELLS
Cylinder
Shell
Cylinder
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VOLUMES BY CYLINDRICAL SHELLS
Example
Find the volume of the solid obtained by rotating
the region enclosed by the curves ysin(x) and
y0 about the y-axis . Find the volume of the
resulting solid.
Disk Method
Shell Method
The method of shells is fundamentally different
from the method of disks.  The method of disks
involves slicing the solid perpendicular to the
axis of revolution to obtain the disks.  However,
the method of shells fills the solid with
cylindrical shells
This demo was developed by Lila F.
Roberts College of Information Mathematical
Sciences Clayton State University Morrow, GA
30260
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VOLUMES BY CYLINDRICAL SHELLS
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VOLUMES BY CYLINDRICAL SHELLS
The volume is given by
Find the surface area
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VOLUMES BY CYLINDRICAL SHELLS
step1
Graph and Identify the region
Draw a line parallel to the rotating line at the
point x
step2
step3
Rotate this line about the rotating line
Find
in terms of
step4
Find
step4
step5
The volume is given by
Note rotating line is y-axis ? dx and we draw a
parallel line to y-axis
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VOLUMES BY CYLINDRICAL SHELLS
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VOLUMES BY CYLINDRICAL SHELLS
T-122
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VOLUMES
T-102
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VOLUMES BY CYLINDRICAL SHELLS
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VOLUMES BY CYLINDRICAL SHELLS
rotating line Parallel to y-axis
CYLINDRICAL SHELLS
The volume is given by
Find the surface area
rotating line Parallel to x-axis
CYLINDRICAL SHELLS
The volume is given by
Find the surface area
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VOLUMES BY CYLINDRICAL SHELLS
Remarks
rotating line Parallel to x-axis
CYLINDRICAL SHELLS (6.2)
rotating line Parallel to y-axis
Remarks
rotating line Parallel to x-axis
DESK(6.1)
rotating line Parallel to y-axis
Cross-section is DISK
Crosssection is WASHER
SHELL Method
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VOLUMES BY CYLINDRICAL SHELLS
T-131
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VOLUMES
T-072
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T-111
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VOLUMES BY CYLINDRICAL SHELLS
T-111
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