Question

An ellipsoid has radii with lengths of `15`, `12`, and `9`. A portion the size of a hemisphere with a radius of `5` is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Answer 1

The remaining volume is `=6230/3pi`

Explanation:

Volume of ellipsoid `=4/3pi*a*b*c`
Volume of a sphere `=4/3pir^3`
Volume of hemisphere `=2/3pir^3`
Remaining volume of ellipsoid `=4/3piabc-2/3pir^3`
`=2/3pi(2abc-r^3)`
`=2/3pi(2*15*12*9-125)`
`=6230/3pi`