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]

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