An ellipsoid has radii with lengths of $4$ , $9$ , and $5$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Question

1333 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-14T16:11:59

$=492.2$

The Volume of an Ellipsoid with radii $=4,9 and 5$

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

$=pi/6(2times9)(2times4)(2times5)$

$=pi/6(18times8times10)$

$=240pi$

$=754$

Volume of an Hemisphere $=2/3(pir^3)$ where $r=5$ is the radius
$=2/3pi(5)^3$

$=2/3pitimes125$

$=(250pi)/3$

$=261.8$

So the remaining volume of the Ellipsoid

$=754-261.8$

$=492.2$

An ellipsoid has radii with lengths of 4 4 , 9 9 , and 5 5 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?