An ellipsoid has radii with lengths of #5 #, #6 #, and #7 #. 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 · 2016-11-19T18:27:22

The remaining volume is #=(590pi)/3#

The volume of an ellipsoid is #=(4piabc)/3#

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

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

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

Here,

#a=5#

#b=6#

#c=7#

#r=5#

Therefore, the remaining volume is

#=((2pi)/3)(2*5*6*7-5^3)#

#=(10pi)/3(84-25)#

#=(590pi)/3#