An ellipsoid has radii with lengths of $12$ , $11$ , and $8$ . A portion the size of a hemisphere with a radius of $8$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-02-06T15:42:22

The volume is $=4289.3 u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*12*11*8-8^3)$

$=2/3pi(2112-64)$

$=2/3pi*2048$

$=4289.3$

An ellipsoid has radii with lengths of 12 12 , 11 11 , and 8 8 . A portion the size of a hemisphere with a radius of 8 8 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?