An ellipsoid has radii with lengths of #3 #, #4 #, and #2 #. 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
Shwetank Mauria
Jun 7, 2016

Remaining volume of the ellipsoid is #(80pi)/3# units.

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 #3#, #4# and #2# is #4/3pixx4xx3xx2=32pi#.

Now as volume of sphere is given by #4/3pir^3#, volume of hemisphere of radius #2# cut from this is #1/2xx4/3pixx2^3=2/3xx8pi=(16pi)/3#

Hence, remaining volume of the ellipsoid is #32pi-(16pi)/3=(80pi)/3#

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