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
marfre
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#

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