Explanation First determine the radius of the solid obtained by rotation and then, calculate the volume by using the appropriate formula. Given: The region y = 32 − 2 x , y = 2 + 4 x , x = 0 is rotated about y -axis. Calculation: Rotating the region enclosed by the region y = 32 − 2 x , y = 2 + 4 x , x = 0 about y -axis produces a solid with two different cross-sections. One is a disk when 2 ≤ y ≤ 22 with radius 1 4 ( y − 2 ) ; for 22 ≤ y ≤ 32 , the cross section is another disk with radius 1 2 ( 32 − y ) ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.3, Problem 42E

To determine

The volume of the solid obtained by rotating the given region about the specified axis.

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Chapter 6.3, Problem 41E

Chapter 6.3, Problem 43E

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The volume of the solid obtained by rotating the given region about the specified axis.

Solution Summary: The author calculates the volume of the solid obtained by rotating the region about the y -axis using the appropriate formula.

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The volume of the solid obtained by rotating the given region about the specified axis.

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Chapter 6 Solutions