Question

An ellipsoid has radii with lengths of `8`, `3`, and `4`. A portion the size of a hemisphere with a radius of `2` is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Answer 1

`368.61` cubic units (approximately)

Explanation:

Formulae you need to remember:
`color(white)("XXX")"Volume"_("ellipsoid")= 4/3 pi * r_x * r_y * r_z`

`color(white)("XXX")"Volume"_("sphere")= 4/3 pi * r^3`

Given ellipsoid has a volume of `4/3pi(8xx3xx4) = 4/3pi * 96`

Given sphere has a volume of `4/3pi (2^2) = 4/3pi *8`

Volume of ellipsoid with sphere removed:
`color(white)("XXX")4/3pi* (96-8) = 352/3 pi ~~368.61`