Question

An ellipsoid has radii with lengths of `8`, `7`, and `9`. A portion the size of a hemisphere with a radius of `8` is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Answer 1

`1038.82\ \text{unit}^3`

Explanation:

The remaining volume of the ellipsoid will be equal to the difference of volume of original ellipsoid with radii `a=8`, `b=7` & `c=9` & the volume of hemi-sphere of radius `r=8` hence the remaining volume of ellipsoid

`\frac{4\pi}{3}abc-2/3\pir^3`

`=\frac{4\pi}{3}(8)(7)(9)-2/3\pi(8)^3`

`=\frac{992\pi}{3}`

`=1038.82\ \text{unit}^3`