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?

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Answer 1 · 2018-02-10T11:10:48

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

The radii of the ellipsoid are $r_{1} = 3, r_{2} = 3, r_{3} = 8$ $r_1=3,r_2=3,r_3=8$ units

The volume of the ellipsoid is $V = \frac{4 \cdot π \cdot r_{1} \cdot r_{2} \cdot r_{3}}{3}$ $V=(4*pi*r_1*r_2*r_3)/3$ or

$V = \frac{4 \cdot π \cdot 3 \cdot 3 \cdot 8}{3} = 301.59$ $V=(4*pi*3*3*8)/3 =301.59$ cubic unit.

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

The volume of the removed hemisphere $V_{h} = \frac{2 \cdot π \cdot r^{3}}{3}$ $V_h=(2*pi*r^3)/3$ or

$V_{h} = \frac{2 \cdot π \cdot 2^{3}}{3} = 16.76$ $V_h=(2*pi*2^3)/3= 16.76$ cubic unit.

The volume of the remaining ellipsoid is $V_{e} = V - V_{h}$ $V_e=V-V_h$ or

$V_{e} = 301.59 - 16.76 = 284.83$ $V_e=301.59-16.76= 284.83$ cunic unit [Ans]

An ellipsoid has radii with lengths of 33 , 33 , and 88 . A portion the size of a hemisphere with a radius of 22 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?