Explanation Given: The given equation is y = x 2 + 2 rotate about the y = − 2 . The figure is shown below: Formula Used: If a washer of inner radius R = f ( y ) a n d o u t e r r a d i u s r = g ( y ) rotated about the y-axis over the given interval a ≤ y ≤ b then the volume of solid revolution is calculated by V = π ∫ a b ( ( R ) 2 − ( r ) 2 ) Calculation: Here, rotating region A about the y = − 2 over the interval 0 ≤ x ≤ 2 produce a solid whose cross sections are washers with outer radius R = 6 − ( − 2 ) = 8 and inner radius r = x 2 + 2 − ( − 2 ) = x 2 + 4 V = π ∫ 0 2 (

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.3, Problem 28E

To determine

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

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Chapter 6.3, Problem 27E

Chapter 6.3, Problem 29E

Chapter 6 Solutions

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Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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

Solution Summary: The author calculates the volume of the solid obtained by rotating region in the given figure about the y = 2.

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

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Chapter 6 Solutions