An ellipsoid has radii with lengths of #14 #, #11 #, and #7 #. A portion the size of a hemisphere with a radius of #9 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2018-07-27T09:26:02

#2988.702\ \text{unit}^3#

The volume #V# of ellipsoid of radii #a=14, b=11# & #c=7# is given as

#V={4\pi}/3abc#

#={4\pi}/3(14)(11)(7)#

#={4312\pi}/3#

The volume #V_1# of hemisphere of radius #r=9# is given as

#V_1=1/2({4\pi}/3r^3)#

#={2\pi}/3r^3#

#={2\pi}/3(9)^3#

#=486\pi#

hence the volume of ellipsoid after removing the volume of hemisphere

#=V-V_1#

#={4312\pi}/3-486\pi#

#={2854\pi}/3#

#=2988.702\ \text{unit}^3#