An ellipsoid has radii with lengths of $5$ , $5$ , and $4$ . A portion the size of a hemisphere with a radius of $3$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Question

1272 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-28T20:19:11

The remaining volume is $=362.3u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*5*5*4-3^3)$

$=2/3pi(200-27)$

$=2/3pi*173$

$=362.3$

An ellipsoid has radii with lengths of 5 5 , 5 5 , and 4 4 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?