# Shell - 6.3 Volumes By Cylindrical Shells This is an...

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6.3 Volumes By Cylindrical Shells This is an alternate method for finding the volume of a solid of revolution that uses cylindrical shells. The strip is parallel to the axis of revolution. This method is sometimes easier to use than the methods discussed in Section 6.2. Volume of Shell ( 29 ( 29 ( 29 thickness height radius average 2 π = height average radius thickness

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Volume: The Shell Method y axis of revolution c d r ( y ) h ( y ) Plane Region Horizontal Strip Solid of Revolution Typical Shell Volume of Typical Shell y y h y r V = ) ( ) ( 2 π where r ( y ) = average radius h ( y )= height y = thickness Volume of Solid = d c dy y h y r V ) ( ) ( 2
Examples Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. Sketch the region and a typical shell. Example One: Example Two: ; 1 , 0 , 0 , 2 = = = = - y y x e x y about the x -axis ; 2 8 , 4 2 2 x x y x x y - = - = about x = -2

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## This note was uploaded on 03/09/2008 for the course CALC 1,2,3 taught by Professor Varies during the Spring '08 term at Lehigh University .

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Shell - 6.3 Volumes By Cylindrical Shells This is an...

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