An ellipsoid has radii with lengths of 6 , 6 , and 3 . A portion the size of a hemisphere with a radius of 6 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer
Nov 12, 2016

Remaining volume is 0

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 6, 6 and 3 is 4/3xxpixx6xx6xx3=144pi.

Now as volume of sphere is given by 4/3pir^3, volume of hemisphere of radius 6 cut from this is 1/2xx4/3pixx6^3=2/3xx216pi=144pi

Hence, remaining volume of the ellipsoid is 144pi-144pi=0