An ellipsoid has radii with lengths of #5 #, #8 #, and #5 #. 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 · 2017-03-01T20:23:06

The remaining volume is #=781.2u^3#

Volume of ellipsoid is #=4/3piabc#

Volume of hemisphere is #=2/3pir^3#

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

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

#=2/3pi(2*5*8*5-3^3)#

#=2/3pi(400-27)#

#=2/3pi*373#

#=781.2#