An ellipsoid has radii with lengths of $5$ , $12$ , and $8$ . A portion the size of a hemisphere with a radius of $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-01-26T17:32:30

The volume is $=1558.3u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*5*12*8-6^3)$

$=2/3pi(960-216)$

$=2/3pi*744$

$=1558.3$

An ellipsoid has radii with lengths of 5 5 , 12 12 , and 8 8 . A portion the size of a hemisphere with a radius of 6 6 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?