An ellipsoid has radii with lengths of $6$ , $5$ , and $7$ . 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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An ellipsoid has radii with lengths of $6$ , $5$ , and $7$ . 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 · 2016-08-08T20:59:00

$=427.25$

Explanation:

The Volume of an Ellipsoid
$=pi/6times$ (major-axis) $times$ (minor axis) $times$ (vertcal-axis)
$=pi/6(2times6)(2times5)(2times7)$
$=pi/6(12times10times14)$
$=280pi$
$=879.65$
Volume of an Hemisphere $=2/3(pir^3)$ where $r=6$ is the radius
$=2/3pi(6)^3$
$=2/3pi(216)$
$=2pi(72)$
$=144pi$
$=452.4$
So the remaining volume of the Ellipsoid
$=879.65-452.4$
$=427.25$

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An ellipsoid has radii with lengths of $6$ , $5$ , and $7$ . 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?

1 Answer

Explanation:

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An ellipsoid has radii with lengths of 6 6 , 5 5 , and 7 7 . 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?

1 Answer

Explanation:

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An ellipsoid has radii with lengths of $6$ , $5$ , and $7$ . 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?