An ellipsoid has radii with lengths of $6$ , $7$ , and $3$ . A portion the size of a hemisphere with a radius of $3$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-12T19:01:51

$=471.3$

The Volume of an Ellipsoid with radii $=6,7 and 3$

$=pi/6times$ (major-axis) $times$ (minor axis) $times$ (vertcal-axis)

$=pi/6(2times7)(2times3)(2times6)$

$=pi/6(14times6times12)$

$=168pi$

$=527.8$

Volume of an Hemisphere $=2/3(pir^3)$ where $r=3$ is the radius
$=2/3pi(3)^3$

$=2/3pi(27)$

$=18pi$

$=56.5$

So the remaining volume of the Ellipsoid

$=527.8-56.5$

$=471.3$

An ellipsoid has radii with lengths of 6 6 , 7 7 , and 3 3 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?