An ellipsoid has radii with lengths of $5$ , $12$ , and $8$ . A portion the size of a hemisphere with a radius of $7$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-14T15:03:45

$=1292.24$

The Volume of an Ellipsoid with radii $=5,12 and 8$

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

$=pi/6(2times12)(2times5)(2times8)$

$=pi/6(24times10times16)$

$=640pi$

$=2010.62$

Volume of an Hemisphere $=2/3(pir^3)$ where $r=7$ is the radius
$=2/3pi(7)^3$

$=2/3pitimes343$

$=228.67pi$

$=718.4$

So the remaining volume of the Ellipsoid

$=2010.62-718.4$

$=1292.24$

An ellipsoid has radii with lengths of 5 5 , 12 12 , and 8 8 . A portion the size of a hemisphere with a radius of 7 7 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?