An ellipsoid has radii with lengths of $5$ , $5$ , 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 · 2017-07-20T10:04:07

The remaining volume is $=366.5u^3$

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The volume of the ellipsoid is $V_e=4/3pi abc$

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

The remaining volume is

$=V_e-V_h$

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

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

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

$=2/3pi*175$

$=366.5u^3$

An ellipsoid has radii with lengths of 5 5 , 5 5 , 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?