An ellipsoid has radii with lengths of #9 #, #8 #, and #6 #. 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?

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Answer 1 · 2017-12-06T12:43:31

The remaining volume is #=1753.1u^3#

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

Here,

#a=9u#

#b=8u#

and #c=6u#

so,

#V_e=4/3pixx9xx8xx6=576pi=1809.6u^3#

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

Here,

#r=3u#

so,

#V_h=2/3pir^3=2/3pixx3^3=56.5u^3#

The remaining volume is

#V_r=V_e-V_h=1809.6-56.5=1753.1u^3#