An ellipsoid has radii with lengths of $2$ , $2$ , and $1$ . A portion the size of a hemisphere with a radius of $1$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Question

1177 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-14T15:56:51

$=14.65$

The Volume of an Ellipsoid with radii $=2,2 and 1$

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

$=pi/6(2times2)(2times1)(2times2)$

$=pi/6(4times2times4)$

$=(16pi)/3$

$=16.75$

Volume of an Hemisphere $=2/3(pir^3)$ where $r=1$ is the radius
$=2/3pi(1)^3$

$=2/3pi$

$=0.67pi$

$=2.1$

So the remaining volume of the Ellipsoid

$=16.75-2.1$

$=14.65$

An ellipsoid has radii with lengths of 2 2 , 2 2 , and 1 1 . A portion the size of a hemisphere with a radius of 1 1 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?