An ellipsoid has radii with lengths of $2$ , $5$ , and $3$ . A portion the size of a hemisphere with a radius of $1$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-10-29T14:58:27

Remaining volume of the ellipsoid is $(118pi)/3$

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

volume of ellipsoid of radii with lengths of $2$ , $5$ and $3$ is $4/3pixx2xx5xx3=40pi$ .

Now as volume of sphere is given by $4/3pir^3$ , volume of hemisphere of radius $1$ cut from this is $1/2xx4/3pixx1^3=2/3xxpi=(2pi)/3$

Hence, remaining volume of the ellipsoid is $40pi-(2pi)/3=(118pi)/3$

An ellipsoid has radii with lengths of 2 2 , 5 5 , and 3 3 . A portion the size of a hemisphere with a radius of 1 1 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?