An ellipsoid has radii with lengths of $8$ , $9$ , and $2$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2016-11-09T06:15:59

Remaining volume of the ellipsoid is $(326pi)/3$

Volume of an ellipsoid with dimensions $a$ , $b$ and $c$ is given by $4/3pixxaxxbxxc$ , hence

volume of ellipsoid of radii with lengths of $8$ , $9$ and $2$ is $4/3pixx8xx9xx2=192pi$ .

Now as volume of sphere is given by $4/3pir^3$ , volume of hemisphere of radius $5$ cut from this is $1/2xx4/3pixx5^3=2/3xx125pi=(250pi)/3$

Hence, remaining volume of the ellipsoid is $192pi-(250pi)/3=(326pi)/3$

An ellipsoid has radii with lengths of 8 8 , 9 9 , and 2 2 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?