Volume of Spheroid

Find the volume of the spheroid formed by the revolution of the area bounded by the ellipse x^2/(a^2)+ y^2/(b^2)=1 about the major axis a.

Kindly Help!

Thanks in advance!

Quote:

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Originally Posted by aqualibra86

Find the volume of the spheroid formed by the revolution of the area bounded by the ellipse x^2/(a^2)+ y^2/(b^2)=1 about the major axis a.

Kindly Help!

Thanks in advance!

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1. The axis a is placed on the x-axis.
A rotation volume with the x-axis as axis of rotation is calculated by:

2. Since you need y² solve the equation of the ellips for y² and use the formula from #1. The bounds of the integral are -a and a. (Why?)

I have did in this way and get V=4/3 (pi) a b^2, just need to know that if this is correct answer .. ?

Quote:

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Originally Posted by aqualibra86

I have did in this way and get V=4/3 (pi) a b^2, just need to know that if this is correct answer .. ?

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Correct! (Clapping)

Thanks alot!