Question

An ellipsoid has radii with lengths of `8`, `9`, and `2`. A portion the size of a hemisphere with a radius of `5` is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Answer 1

Remaining volume of the ellipsoid is `(326pi)/3`

Explanation:

Volume of an ellipsoid with dimensions `a`, `b` and `c` is given by `4/3pixxaxxbxxc`, hence

volume of ellipsoid of radii with lengths of `8`, `9` and `2` is `4/3pixx8xx9xx2=192pi`.

Now as volume of sphere is given by `4/3pir^3`, volume of hemisphere of radius `5` cut from this is `1/2xx4/3pixx5^3=2/3xx125pi=(250pi)/3`

Hence, remaining volume of the ellipsoid is `192pi-(250pi)/3=(326pi)/3`