An ellipsoid has radii with lengths of $3$ , $4$ , and $1$ . 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?

Question

1215 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-10T09:26:58

The remaining volume is $=33.5 u^3$

Volume of ellipsoid is $=4/3piabc$

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

Remaining volume $=4/3piabc-2/3pir^3$

$=2/3pi(2abc-r^3)$

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

$=2/3pi(24-28)$

$=2/3pi*16$

$=33.5$

An ellipsoid has radii with lengths of 3 3 , 4 4 , and 1 1 . 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?