An ellipsoid has radii with lengths of $2$ , $1$ , and $6$ . A portion the size of a hemisphere with a radius of $2$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-06-07T13:15:44

Remaining volume of the ellipsoid is $(32pi)/3$

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

volume of ellipsoid of radii with lengths of $2$ , $1$ and $6$ is $4/3pixx2xx1xx6=16pi$ .

Now as volume of sphere is given by $4/3pir^3$ , volume of hemisphere of radius $2$ cut from this is $1/2xx4/3pixx2^3=2/3xx8pi=(16pi)/3$

Hence, remaining volume of the ellipsoid is $16pi-(16pi)/3=(32pi)/3$

An ellipsoid has radii with lengths of 2 2 , 1 1 , and 6 6 . A portion the size of a hemisphere with a radius of 2 2 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?