Question

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

Answer 1

Remaining volume is `0`

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 `6`, `6` and `3` is `4/3xxpixx6xx6xx3=144pi`.

Now as volume of sphere is given by `4/3pir^3`, volume of hemisphere of radius `6` cut from this is `1/2xx4/3pixx6^3=2/3xx216pi=144pi`

Hence, remaining volume of the ellipsoid is `144pi-144pi=0`