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Volume of an ellipsoid Suppose that the ellipse x2/a2 +

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 79E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 79E

Volume of an ellipsoid Suppose that the ellipse \(x^2/a^2 + y^2/b^2 = 1\) is revolved about the x-axis. What is the volume of the ellipsoid that is generated? Is the volume different if the same ellipse is revolved about the y-axis?

Step-by-Step Solution:

Solution 79E

Step 1 :

Given : .

a. To calculate the volume of the ellipsoid, we know that the volume of the solid generated by revolving the curve y=f(x)  about the x-axis is given as follows

Here the volume generated by is calculated by putting and using the limit from (-a,a) as follows


   

   

   

   

   

Hence the volume generated by revolving the ellipse about the x-axis is .

b. To calculate the volume of the solid generated by  revolving the curve    about the y-axis is given as follows


Here the volume generated by
is calculated by putting and using the limit from (-b,b) as follows


   

   

   

   

   

Hence the volume generated by the ellipse revolved around the
y-axis is .

Yes, the volume is different if ellipse is revolved about y-axis.


   

Step 2 of 1

Chapter 10.4, Problem 79E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

This full solution covers the following key subjects: Volume, axis, Ellipse, ellipsoid, revolved. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 79E from 10.4 chapter was answered, more than 388 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 79E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Volume of an ellipsoid Suppose that the ellipse x2/a2 + y2/b2 = 1 is revolved about the x-axis. What is the volume of the ellipsoid that is generated? Is the volume different if the same ellipse is revolved about the y-axis?” is broken down into a number of easy to follow steps, and 41 words.

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Volume of an ellipsoid Suppose that the ellipse x2/a2 +