An ellipsoid has radii with lengths of #1 #, #3 #, and #2 #. 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 · 2018-07-22T07:00:09

The remaining volume is #=8.38u^3#

The volume of an ellipsoid is

#V_e=4/3piabc#

The volume of a hemisphere is

#V_h=1/2*4/3pir^3=2/3pir^3#

Here,

#a=1#

#b=3#

#c=2#

#r=2#

The remaining volume is

#V_r=V_e-V_h#

#=4/3piabc-2/3pir^3#

#=2/3pi(2abc-r^3)#

#=2/3pi(2*1*3*2-2^3)#

#=2/3pi*(12-8)#

#=8/3pi#

#=8.38u^3#