An ellipsoid has radii with lengths of $6$ , $8$ , and $8$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-02-14T07:35:30

The remaining volume is $=1346.7u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*6*8*8-5^3)$

$=2/3pi(768-125)$

$=2/3pi*643$

$=1346.7$

An ellipsoid has radii with lengths of 6 6 , 8 8 , and 8 8 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?