An ellipsoid has radii with lengths of $6$ , $7$ , and $12$ . 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 $6$ , $7$ , and $12$ . 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 · 2016-08-10T23:21:45

$=1849.35$

Explanation:

The Volume of an Ellipsoid with radii $=6,7 and 12$
$=pi/6times$ (major-axis) $times$ (minor axis) $times$ (vertcal-axis)
$=pi/6(2times12)(2times7)(2times6)$
$=pi/6(24times14times12)$
$=672pi$
$=2111.15$
Volume of an Hemisphere $=2/3(pir^3)$ where $r=5$ is the radius
$=2/3pi(5)^3$
$=2/3pi(125)$
$=250/3pi$
$=261.8$
So the remaining volume of the Ellipsoid
$=2111.15-261.8$
$=1849.35$

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An ellipsoid has radii with lengths of $6$ , $7$ , and $12$ . 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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An ellipsoid has radii with lengths of 6 6 , 7 7 , and 12 12 . 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 $6$ , $7$ , and $12$ . 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?