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Centroid of ellipse

Half of an ellipse is centered with x, y, and z axis' passing through. The nose extends out towards the y axis at a distance b. It's circular base has radial height 'a' from the x axis.
Locate the centroid of the ellipsoid of revolution whose equation is y^2/b^2 + z^2/a^2 = 1.

Solution Preview

I am assuming that we are taking the half-ellipse in the y-z plane given by the equation,

y^2/b^2 + z^2/a^2 = 1

2b is the length of the major axis (along y), and 2a is the length of the minor axis (along z)

and rotate it around the z-axis to get an ellipsoid.

We will use the second theorem of ...

Solution Summary

This solution is provided in 286 words. It discusses the second theorem of Pappus to find volume and calculate the centroid.