Question

An ellipsoid has radii with lengths of `2`, `1`, 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

The remaining volume `=20/3pi`

Explanation:

The volume of the ellipsoid is `4/3piabc`

The volume of a sphere `=4/3pir^3`

Volume of a hemisphere `=2/3pir^3`

Remaining volume `=4/3piabc-2/3pir^3=4/3pi(abc-r^3)`

`4/3pi(2*1*3-1^3)=20/3pi`