Question

An ellipsoid has radii with lengths of `6`, `11`, and `8`. 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 `=(1862pi)/3`

Explanation:

The volume of an ellipsoid is `(4/3)piabc`

The volume of a sphere is `(4/3)pir^3`

The volume of a hemisphere `=1/2*(4/3)pir^3=(2/3)pir^3`

The remaining volume `=(4/3)piabc-(2/3)pir^3`
`=(2pi)/3(2abc-r^3)`
`=(2pi)/3(2*6*11*8-5^3)`
`=(2pi)/3(931)=(1862pi)/3`