Objective Find the volume of a solid of revolution using the Shell method Compare to the disk method Miss Battaglia AP Calculus Alternative to finding volume of a solid of revolution Called the shell method because it uses cylindrical shells ID: 369446
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Slide1
7-3 Volume: The Shell MethodObjective: Find the volume of a solid of revolution using the Shell method. Compare to the disk method.
Miss
Battaglia
AP CalculusSlide2
Alternative to finding volume of a solid of revolution. Called the shell method because it uses cylindrical shells.
The Shell MethodSlide3
To find the volume of a solid of revolution with the
shell method
, use of the following
Horizontal Axis of Revolution
Vertical Axis of RevolutionThe Shell MethodSlide4
Find the volume of the solid of revolution formed by revolving the region bounded by y=x-x3 and the x-axis (0<
x
<
1) about the y-axis.
Using the Shell Method to Find VolumeSlide5
Find the volume of the solid of revolution formed by revolving the region bounded by the graph of and the y-axis (0<
y
<
1) about the x-axis.
Using the Shell Method to Find VolumeSlide6
Disk method: representative rectangle is always perpendicular to the axis of revolution.
Shell method:
representative rectangle is always parallel to the axis of revolution.
Comparison of Disk and Shell MethodsSlide7
Find the volume of the solid formed by revolving the region bounded by the graph of y=x2+1, y=0, x=0, and x=1 about the y-axis.
Shell Method More PreferableSlide8
A pontoon is to be made in the shape shown in the figure ***ADD FIGURE. The pontoon is designed by rotating the graph of
Volume of a PontoonSlide9
Find the volume of a solid formed by revolving the region bounded by the graphs of y=x3+x+1, y=1, x=1 about the line x=2.
Shell Method NecessarySlide10
Classwork/Homework