An ellipsoid has radii with lengths of $14$ , $12$ , and $6$ . A portion the size of a hemisphere with a radius of $9$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-02-12T10:44:28

The answer is $=2695.5u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*14*12*6-9^3)$

$=2/3pi(2016-729)$

$=2/3pi*1287$

$=2695.5$

An ellipsoid has radii with lengths of 14 14 , 12 12 , and 6 6 . A portion the size of a hemisphere with a radius of 9 9 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?