An ellipsoid has radii with lengths of 8 , 9 , and 2 . A portion the size of a hemisphere with a radius of 5 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer
Nov 9, 2016

Remaining volume of the ellipsoid is (326pi)/3

Explanation:

Volume of an ellipsoid with dimensions a, b and c is given by 4/3pixxaxxbxxc, hence

volume of ellipsoid of radii with lengths of 8, 9 and 2 is 4/3pixx8xx9xx2=192pi.

Now as volume of sphere is given by 4/3pir^3, volume of hemisphere of radius 5 cut from this is 1/2xx4/3pixx5^3=2/3xx125pi=(250pi)/3

Hence, remaining volume of the ellipsoid is 192pi-(250pi)/3=(326pi)/3