An ellipsoid has radii with lengths of $2$ , $8$ , and $5$ . 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 · 2017-01-30T06:38:18

The volume is $=278.6 u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

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

$=2/3pi(160-27)$

$=2/3pi*133$

$=278.6$

An ellipsoid has radii with lengths of 2 2 , 8 8 , and 5 5 . 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?