An ellipsoid has radii with lengths of #3 #, #3 #, and #8 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2018-02-10T11:10:48

The volume of the remaining ellipsoid is #284.83# cunic unit.

The radii of the ellipsoid are #r_1=3,r_2=3,r_3=8# units

The volume of the ellipsoid is #V=(4*pi*r_1*r_2*r_3)/3# or

#V=(4*pi*3*3*8)/3 =301.59# cubic unit.

The radii of the removed hemisphere #r=2# unit

The volume of the removed hemisphere #V_h=(2*pi*r^3)/3# or

#V_h=(2*pi*2^3)/3= 16.76# cubic unit.

The volume of the remaining ellipsoid is #V_e=V-V_h# or

#V_e=301.59-16.76= 284.83# cunic unit [Ans]