An ellipsoid has radii with lengths of $8$ , $9$ , and $2$ . 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 · 2017-04-07T18:14:29

$174 pi ~~ 546.637 " units"^3$

Volume of an ellipsoid $V_(ellipsoid) = 4/3 pi abc$ where $a, b, c$ are the radii.

Volume of a hemisphere is half the volume of a sphere $V_(hemisphere) = 1/2*4/3 pi r^3 = 2/3 pi r^3$

$V_(ellipsoid) - V_(hemisphere) = 4/3 pi *8*9*2 - 2/3 pi 3^3$

$= 192 pi - 18 pi = 174 pi$

$V_(ellipsoid) - V_(hemisphere) = 174 pi ~~ 546.637 " units"^3$

An ellipsoid has radii with lengths of 8 8 , 9 9 , and 2 2 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?