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Prove a property of the volume of the solid of revolution formed by an ellipse

by RoRi
  1. Prove that the volume of the solid of revolution obtained by rotating the ellipse

        \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]

    about its major axis is ab^2 times the volume of the unit sphere.

  2. What is the result in the case that the ellipse is rotated about its minor axis?

Incomplete.

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