An ellipsoid has radii with lengths of $8$ , $7$ , and $6$ . 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 · 2017-02-05T07:51:03

The volume is $=1145.6 u^3$

Volume of ellipsoid is $=4/3piabc$

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

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

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

$=2/3pi(2*8*7*6-5^3)$

$=2/3pi(672-125)$

$=2/3pi*547$

$=1145.6$

An ellipsoid has radii with lengths of 8 8 , 7 7 , and 6 6 . 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?