An ellipsoid has radii with lengths of $6$ , $6$ , and $3$ . A portion the size of a hemisphere with a radius of $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-12T17:08:09

Remaining volume is $0$

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

volume of ellipsoid of radii with lengths of $6$ , $6$ and $3$ is $4/3xxpixx6xx6xx3=144pi$ .

Now as volume of sphere is given by $4/3pir^3$ , volume of hemisphere of radius $6$ cut from this is $1/2xx4/3pixx6^3=2/3xx216pi=144pi$

Hence, remaining volume of the ellipsoid is $144pi-144pi=0$

An ellipsoid has radii with lengths of 6 6 , 6 6 , and 3 3 . A portion the size of a hemisphere with a radius of 6 6 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?