An ellipsoid has radii with lengths of 8 , 9 , and 2 . A portion the size of a hemisphere with a radius of 3 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer
Apr 7, 2017

174 pi ~~ 546.637 " units"^3

Explanation:

Volume of an ellipsoid V_(ellipsoid) = 4/3 pi abc where a, b, c are the radii.

Volume of a hemisphere is half the volume of a sphere V_(hemisphere) = 1/2*4/3 pi r^3 = 2/3 pi r^3

V_(ellipsoid) - V_(hemisphere) = 4/3 pi *8*9*2 - 2/3 pi 3^3

= 192 pi - 18 pi = 174 pi

V_(ellipsoid) - V_(hemisphere) = 174 pi ~~ 546.637 " units"^3