An ellipsoid has radii with lengths of $8$ , $9$ , and $5$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2017-03-14T06:17:57

The remaining volume is $=1246.2u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*8*9*5-5^3)$

$=2/3pi(720-125)$

$=2/3pi*595$

$=1246.2$

An ellipsoid has radii with lengths of 8 8 , 9 9 , and 5 5 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?