An ellipsoid has radii with lengths of $3$ , $4$ , and $2$ . 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 · 2016-06-07T13:12:01

Remaining volume of the ellipsoid is $(80pi)/3$ units.

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

volume of ellipsoid of radii with lengths of $3$ , $4$ and $2$ is $4/3pixx4xx3xx2=32pi$ .

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 $32pi-(16pi)/3=(80pi)/3$

An ellipsoid has radii with lengths of 3 3 , 4 4 , and 2 2 . 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?