An ellipsoid has radii with lengths of #6 #, #4 #, and #8 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2017-12-20T13:15:53

The remaining volume is #=787.49u^3#

The volume of an ellipsoid is #V_e=4/3abc# where #a#, #b#, and #c# are the lengths.

Here,

#a=6u#

#b=4u#

and #c=8u#

so,

#V_e=4/3pixx6xx4xx8=576pi=804.25u^3#

The volume of a hemisphere is #V_h=2/3pir^3# where #r# is rhe radius

Here,

#r=2u#

so,

#V_h=2/3pir^3=2/3pixx2^3=16.76u^3#

The remaining volume is

#V_r=V_e-V_h=804.25-16.76=787.49u^3#