An ellipsoid has radii with lengths of $9$ , $12$ , and $10$ . 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 · 2017-06-25T09:57:18

The remaining volume is $=4262.1u^3$

The volume of the ellipsoid is

$V_e=4/3piabc$

The volume of the hemisphere is

$V_h=1/2*4/3pir^3$

The remaining volume is

$V_e-V_h=4/3piabc-2/3pir^3$

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

$=2/3pi(2*9*12*10-5^3)$

$=4262.1$

An ellipsoid has radii with lengths of 9 9 , 12 12 , and 10 10 . 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?