An ellipsoid has radii with lengths of #3 #, #6 #, 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 · 2018-08-07T08:50:13

The volume remaining is #=320.4u^3#

The volume of an ellipsoid is

#V_e=4/3piabc#

The volume of a hemisphere is

#V_h=1/2*4/3pir^3=2/3pir^3#

Here,

#a=3#

#b=6#

#c=5#

#r=3#

The remaining volume is

#V_r=V_e-V_h#

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

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

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

#=2/3pi*(180-27)#

#=(2*153)/3pi#

#=320.4u^3#