Question

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

Answer 1

Remaining volume of the ellipsoid is `(32pi)/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`, `1` and `6` is `4/3pixx2xx1xx6=16pi`.

Now as volume of sphere is given by `4/3pir^3`, volume of hemisphere of radius `2` cut from this is `1/2xx4/3pixx2^3=2/3xx8pi=(16pi)/3`

Hence, remaining volume of the ellipsoid is `16pi-(16pi)/3=(32pi)/3`