An ellipsoid has radii with lengths of $3$ , $4$ , and $7$ . 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 · 2016-12-10T10:06:20

THe answer is $=38pi=119.4$

The volume of an ellipsoid is $4/3piabc$

The volume of a hemisphere is $=2/3pir^3$

The remaining volume $=4/3piabc-2/3pir^3$

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

$=2/3pi(3*4*7-3^3)$

$=2/3pi(84-27)$

$=2/3pi*57$

$=2*19pi$

$=38pi=119.4$

An ellipsoid has radii with lengths of 3 3 , 4 4 , and 7 7 . 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?