An ellipsoid has radii with lengths of #6 #, #9 #, and #5 #. 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?

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Answer 1 · 2018-07-26T16:07:22

#216\pi\ \text{unit}^3#

The volume #V# of ellipsoid of radii #a=6, b=9# & #c=5# is given as

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

#={4\pi}/3(6)(9)(5)#

#=360\pi#

The volume #V_1# of hemisphere of radius #r=6# is given as

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

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

#={2\pi}/3(6)^3#

#=144\pi#

hence the volume of ellipsoid after removing the volume of hemisphere

#=V-V_1#

#=360\pi-144\pi#

#=216\pi\ \text{unit}^3#