An ellipsoid has radii with lengths of $14$ , $4$ , and $6$ . A portion the size of a hemisphere with a radius of $2$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-01-22T13:50:57

The remaining volume is $=1328/3pi$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*14*4*6-2^3)$

$=2/3pi(672-8)$

$=2/3pi*664$

$=1328/3pi$

An ellipsoid has radii with lengths of 14 14 , 4 4 , and 6 6 . A portion the size of a hemisphere with a radius of 2 2 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?