An ellipsoid has radii with lengths of $2$ , $1$ , and $3$ . A portion the size of a hemisphere with a radius of $1$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-11T13:51:17

The remaining volume $=20/3pi$

The volume of the ellipsoid is $4/3piabc$

The volume of a sphere $=4/3pir^3$

Volume of a hemisphere $=2/3pir^3$

Remaining volume $=4/3piabc-2/3pir^3=4/3pi(abc-r^3)$

$4/3pi(2*1*3-1^3)=20/3pi$

An ellipsoid has radii with lengths of 2 2 , 1 1 , and 3 3 . A portion the size of a hemisphere with a radius of 1 1 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?