An ellipsoid has radii with lengths of #6 #, #12 #, and #9 #. A portion the size of a hemisphere with a radius of #7 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-01-15T10:06:00

The volume is #=1996u^3#

Volume of ellipsoid is #=4/3piabc#

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

Volume of remaining solid #=4/3piabc-2/3pir^3#

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

#=2/3pi(2*6*12*9-7^3)#

#=2/3pi(1296-343)#

#=2/3pi*953=1996u^3#