Explanation Obtain the radius of the disk produced by rotation and use that to determine the volume of the ellipsoid, Given: Rotating the region R given in the figure 15 about the y -axis has volume 4 3 π a 2 b Calculation: Given that the region R given in the figure 15 is rotated about the y -axis. Therefore, on slicing the portion of the ellipse in the first and fourth quadrants horizontally and then rotating the slices about the y -axis produces disks that have radius a 2 − a 2 y 2 b 2 . Hence the volume is given by π ∫ − b b ( a 2 − a 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 61E

To determine

To show that the solid (an ellipsoid) obtained by rotating the region $R$ given in the figure 15, about the $y$ -axis has volume $\frac{4}{3} π a^{2} b$

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Chapter 6.4, Problem 60E

Chapter 6.4, Problem 62E

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Chapter 6 Solutions

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To show that the solid (an ellipsoid) obtained by rotating the region R given in the figure 15, about the y -axis has volume 4 3 π a 2 b

Solution Summary: The author explains that the volume of the ellipsoid obtained by rotating the region R given in the figure 15 is 4 3 a 2 b.

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To show that the solid (an ellipsoid) obtained by rotating the region $R$ given in the figure 15, about the $y$ -axis has volume $\frac{4}{3} π a^{2} b$

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Chapter 6 Solutions

To show that the solid (an ellipsoid) obtained by rotating the region R given in the figure 15, about the y -axis has volume 4 3 π a 2 b

Solution Summary: The author explains that the volume of the ellipsoid obtained by rotating the region R given in the figure 15 is 4 3 a 2 b.

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To show that the solid (an ellipsoid) obtained by rotating the region R given in the figure 15, about the y-axis has volume 43πa2b

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Chapter 6 Solutions

To show that the solid (an ellipsoid) obtained by rotating the region $R$ given in the figure 15, about the $y$ -axis has volume $\frac{4}{3} π a^{2} b$