An ellipsoid has radii with lengths of #3 #, #4 #, and #7 #. 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 · 2016-12-10T10:06:20

THe answer is #=38pi=119.4#

The volume of an ellipsoid is #4/3piabc#

The volume of a hemisphere is #=2/3pir^3#

The remaining volume #=4/3piabc-2/3pir^3#

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

#=2/3pi(3*4*7-3^3)#

#=2/3pi(84-27)#

#=2/3pi*57#

#=2*19pi#

#=38pi=119.4#