An ellipsoid has radii with lengths of $2$ , $2$ , and $3$ . 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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An ellipsoid has radii with lengths of $2$ , $2$ , and $3$ . 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 · 2018-06-12T15:18:21

$color(blue)("volume"=(32pi)/3" units"^3)$

Explanation:

The volume of an ellipsoid is given by:

$V=4/3pi*a*b*c$

Where $a, b, c$ are the radii of the ellipsoid.

The volume of a hemisphere is half the volume of a sphere:

Volume of a sphere is:

$V=4/3pir^3$

So volume of hemisphere is:

$V=2/3pir^3$

To find the volume of the ellipsoid when the hemisphere is removed, we just find the volume of the ellipsoid and subtract the volume of the hemisphere:

$V=4/3pi*a*b*c-2/3pir^3$

$V=2/3pi(2abc-r^3)$

Substituting values:

$V=2/3pi(2*2*2*3-2^3)$

$V=2/3pi(16)$

$V=(32pi)/3$

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

1 Answer

Explanation:

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Science

Math

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

1 Answer

Explanation:

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