L11 - Volume Calculation by the Method of Cylindircal Shells

L11 - Volume Calculation by the Method of Cylindircal...

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Volumes By Cylindrical Shells (Section 6.2) When we used the method of disks or washers to find the volume of a solid of revolution, we sliced perpendicular to the axis of revolution. We are now going to slice parallel to the axis of revolution. This method is called the method of cylindrical shells. Remember we slice the region and then revolve it to get the volume. DEF The Shell Method The volume of a solid of revolution whose cross-sections are cylindrical shells of radius r and height h is: V 2 ( r )( h ) dx a b
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Ex. Find the volume of the solid generated by revolving the
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Unformatted text preview: region bounded by y x 2 3 , the x-axis, and x = 8 around: a. the x-axis b. x = 8 c. the y-axis d. y = -1 e. y = 6 f. x = -1 Do: 1. Let R be the region in the xy plane bounded by . Set up the integral for the volume of the solid obtained by rotating R about the y-axis, using cylindrical slices. 2. Let R be the region in the xy plane bounded by y 2 x 2 and y 3 x 1 . Set up the integral for the volume of the solid obtained by rotating R about the x-axis, using cylindrical slices. y 4 x , x 2, and y 1 4...
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L11 - Volume Calculation by the Method of Cylindircal...

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