An ellipsoid has radii with lengths of #6 #, #8 #, and #5 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-02-13T14:04:00

The remaining volume is #=552.9 u^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*6*8*5-6^3)#

#=2/3pi(480-216)#

#=2/3pi*264#

#=552.9#