An ellipsoid has radii with lengths of $2$ , $5$ , and $4$ . A portion the size of a hemisphere with a radius of $3$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-03-01T06:54:16

The remaining volume is $=111 u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*2*5*4-3^3)$

$=2/3pi(80-27)$

$=2/3pi*53$

$=111$

An ellipsoid has radii with lengths of 2 2 , 5 5 , and 4 4 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?