Question

An ellipsoid has radii with lengths of `2`, `5`, and `3`. A portion the size of a hemisphere with a radius of `1` is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Answer 1

Remaining volume of the ellipsoid is `(118pi)/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 `2`, `5` and `3` is `4/3pixx2xx5xx3=40pi`.

Now as volume of sphere is given by `4/3pir^3`, volume of hemisphere of radius `1` cut from this is `1/2xx4/3pixx1^3=2/3xxpi=(2pi)/3`

Hence, remaining volume of the ellipsoid is `40pi-(2pi)/3=(118pi)/3`