An ellipsoid has radii with lengths of $6$ , $11$ , and $8$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-11T18:58:33

The remaining volume is $=(1862pi)/3$

The volume of an ellipsoid is $(4/3)piabc$

The volume of a sphere is $(4/3)pir^3$

The volume of a hemisphere $=1/2*(4/3)pir^3=(2/3)pir^3$

The remaining volume $=(4/3)piabc-(2/3)pir^3$
$=(2pi)/3(2abc-r^3)$
$=(2pi)/3(2*6*11*8-5^3)$
$=(2pi)/3(931)=(1862pi)/3$

An ellipsoid has radii with lengths of 6 6 , 11 11 , and 8 8 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?