Explanation The Shell Method is best suited for this approach considering that the rotation of the region around x = 2 produces a solid with a single cross-section on performing a vertical slice. Given: Region B is rotated about x = 2 Calculation: Since the vertical slice of region B produces a solid with a single cross section, while a horizontal slice will produce two different cross-sections, we use the Shell method as it uses the vertical slice to calculate the volume. The vertical slice is parallel to the axis of rotation in this case. Each shell has radius 2 − x and height x 2 + 2 . The volume of the resulting solid will be V = 2 π ∫ 0 2 ( 2 − x ) ( x 2 + 2 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 43E

To determine

The volume obtained by rotating the region $B$ about the given axis using any convenient method, among the Disk and Shell Methods

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Chapter 6.4, Problem 42E

Chapter 6.4, Problem 44E

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The volume obtained by rotating the region B about the given axis using any convenient method, among the Disk and Shell Methods

Solution Summary: The author explains that the volume obtained by rotating the region B about the given axis is best determined by the Shell Method in this case.

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The volume obtained by rotating the region $B$ about the given axis using any convenient method, among the Disk and Shell Methods

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Chapter 6 Solutions