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

Chapter 9, Problem 79E

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QUESTION:

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?

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QUESTION:

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?

ANSWER:

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


   

   

   

   

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