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Centroid of ellipse

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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.

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Solution Summary

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

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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 ...

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