LA6b-ShellsV2

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Florida International University *

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2312

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Mathematics

Date

Apr 3, 2024

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MAC 2312 Learning Activity #6b Volumes by Shells Solids of Revolution Names: Group #: 1. The region between the curve y = x √ x 3 + 1 and the x -axis on [0 , 3] is rotated about the y -axis. used the shells’ method to find the volume of the generated solid. (Could you have alternatively used the disks or washers method in this problem too?) 1 2 3 x y Page 1 of 4

MAC 2312 Learning Activity #6b Volumes by Shells Solids of Revolution 2. The region between the curves y = − √ x +2 and x = 1 and the x -axis is rotated about the y -axis . Use the shell method to find the volume of the generated solid. (What does this solid look like?) 1 2 3 4 1 x y Page 2 of 4

MAC 2312 Learning Activity #6b Volumes by Shells Solids of Revolution 3. Use the shell method to find the volume of the solid generated by revolving the region bounded by f ( x ) = − sin( x 2 ), the x -axis and the vertical line x = p π/ 2 about the y -axis. x = p π/ 2 1 − 1 x y Page 3 of 4

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MAC 2312 Learning Activity #6b Volumes by Shells Solids of Revolution 4. Find the volume of the solid generated by revolving the region bounded by y = x 2 , x = 1, and y = 0 about the line y = − 1. 1 − 1 x y Page 4 of 4

LA6b-ShellsV2

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