How would I go about computing the volume of an ellipsoid with spherical caps removed and a cylindrical hole through it?

samuelaplc 2022-10-01 Answered
Volume of Ellipsoid with a hole
How would I go about computing the volume of an ellipsoid with spherical caps removed and a cylindrical hole through it? I'm thinking about finding dV of a cross section (the ellipsoid has a circular horizontal cross section). Would this be the best way to go? I need to find if the volume is dependent on the radius of the sphere.
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Answers (1)

Elisa Spears
Answered 2022-10-02 Author has 9 answers
Explanation:
Assuming x is the major axis, you can integrate the ellipsoid using a triple integral while setting your x limits to be d x e, assuming the "caps" of the ellipsoid are cut off at the planes x = d and x = e. After that you can simply subtract the volume of the cylinder that was cut out.
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