Thread: 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!

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!

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 .. ?

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 .. ?

Correct!

Thanks alot!