An ellipsoid has radii with lengths of $15$ , $12$ , and $9$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of $15$ , $12$ , and $9$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-08T18:37:24

The remaining volume is $=6230/3pi$

Explanation:

Volume of ellipsoid $=4/3pi*a*b*c$
Volume of a sphere $=4/3pir^3$
Volume of hemisphere $=2/3pir^3$
Remaining volume of ellipsoid $=4/3piabc-2/3pir^3$
$=2/3pi(2abc-r^3)$
$=2/3pi(2*15*12*9-125)$
$=6230/3pi$

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An ellipsoid has radii with lengths of $15$ , $12$ , and $9$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

An ellipsoid has radii with lengths of 15 15 , 12 12 , and 9 9 . A portion the size of a hemisphere with a radius of 5 5 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 $15$ , $12$ , and $9$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?