An ellipsoid has radii with lengths of $8$ , $6$ , and $5$ . A portion the size of a hemisphere with a radius of $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2016-08-28T13:21:33

$=988.54$

The Volume of an Ellipsoid with radii $=8,6 and 5$

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

$=pi/6(2times8)(2times5)(2times6)$

$=pi/6(16times10times12)$

$=320pi$

$=1005.3$

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

$=2/3pitimes8$

$=16/3pi$

$=16.76$

So the remaining volume of the Ellipsoid

$=1005.3-16.76$

$=988.54$

An ellipsoid has radii with lengths of 8 8 , 6 6 , and 5 5 . A portion the size of a hemisphere with a radius of 2 2 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?