An ellipsoid has radii with lengths of $8$ , $6$ , and $4$ . A portion the size of a hemisphere with a radius of $2$ is removed from the ellipsoid. What is the volume of the remaining ellipsoid?

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An ellipsoid has radii with lengths of $8$ , $6$ , and $4$ . A portion the size of a hemisphere with a radius of $2$ is removed from the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2018-01-28T01:17:57

$250 2/3pi=V$

Explanation:

Remember that the formula for the volume of an ellipsoid is:
$V=4/3pi(r_1*r_2*r_3)$

We plug the given radii lengths to find the volume.

=> $V=4/3pi(8*6*4)$
=> $V=4/3pi192$
=> $V=256pi$

Now, a hemisphere with a radius of 2 is removed from the ellipsoid.
We have to subtract the volume of the hemisphere from the volume of the ellipsoid.

A volume of a hemisphere is: $1/2*4/3*pir^3$ We now solve for the volume.
=> $V=1/2*4/3*pir^3$
=> $V=4/6*pi(2)^3$
=> $V=4/6*pi8$
=> $V=16/3*pi$ We now subtract.

=> $256pi-16/3pi=V$

=> $pi(256-16/3)=V$
=> $pi(752/3)=V$
=> $250 2/3pi=V$
That is our answer!

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An ellipsoid has radii with lengths of $8$ , $6$ , and $4$ . A portion the size of a hemisphere with a radius of $2$ is removed from the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer

Explanation:

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An ellipsoid has radii with lengths of 8 8 , 6 6 , and 4 4 . A portion the size of a hemisphere with a radius of 2 2 is removed from the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer

Explanation:

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An ellipsoid has radii with lengths of $8$ , $6$ , and $4$ . A portion the size of a hemisphere with a radius of $2$ is removed from the ellipsoid. What is the volume of the remaining ellipsoid?