An ellipsoid has radii with lengths of #2 #, #2 #, and #3 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
1 Answer
Jun 12, 2018
Explanation:
The volume of an ellipsoid is given by:
Where
The volume of a hemisphere is half the volume of a sphere:
Volume of a sphere is:
So volume of hemisphere is:
To find the volume of the ellipsoid when the hemisphere is removed, we just find the volume of the ellipsoid and subtract the volume of the hemisphere:
Substituting values:
