An ellipsoid has radii with lengths of $6$ , $8$ , and $12$ . A portion the size of a hemisphere with a radius of $3$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2017-02-16T17:11:20

THe remaining volume is $=2356.2u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

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

$=2/3pi(1152-27)$

$=2/3pi*1125$

$=2356.2$

An ellipsoid has radii with lengths of 6 6 , 8 8 , and 12 12 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?