Question

An ellipsoid has radii with lengths of `3`, `6`, and `1`. A portion the size of a hemisphere with a radius of `2` is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Answer 1

`56/3 pi`

Explanation:

The volume of the original ellipsoid was `4/3 pi xx 3 xx 6 xx 1 =24 pi`
The volume taken away is `1/2 xx 4/3 pi xx 2^3 = 16/3 pi`
Thus the volume remaining is `24 pi - 16/3 pi = 56/3 pi`