An ellipsoid has radii with lengths of $12$ , $16$ , and $8$ . A portion the size of a hemisphere with a radius of $8$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-13T12:47:01

$=5361.67$

The Volume of an Ellipsoid with radii $=12,16 and 8$

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

$=pi/6(2times16)(2times8)(2times12)$

$=pi/6(32times16times24)$

$=2048pi$

$=6434$

Volume of an Hemisphere $=2/3(pir^3)$ where $r=8$ is the radius
$=2/3pi(8)^3$

$=2/3pitimes512$

$=341.34pi$

$=1072.34$

So the remaining volume of the Ellipsoid

$=6434-1072.34$

$=5361.67$

An ellipsoid has radii with lengths of 12 12 , 16 16 , and 8 8 . A portion the size of a hemisphere with a radius of 8 8 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?