An ellipsoid has radii with lengths of #9 #, #12 #, and #10 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-06-25T09:57:18

The remaining volume is #=4262.1u^3#

The volume of the ellipsoid is

#V_e=4/3piabc#

The volume of the hemisphere is

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

The remaining volume is

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

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

#=2/3pi(2*9*12*10-5^3)#

#=4262.1#