An ellipsoid has radii with lengths of $5$ , $4$ , and $8$ . A portion the size of a hemisphere with a radius of $3$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-14T18:22:18

$=613.65$

The Volume of an Ellipsoid with radii $=5,4 and 8$

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

$=pi/6(2times8)(2times4)(2times5)$

$=pi/6(16times8times10)$

$=(640pi)/3$

$=670.2$

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

$=2/3pitimes27$

$=18pi$

$=56.55$

So the remaining volume of the Ellipsoid

$=670.2-56.55$

$=613.65$

An ellipsoid has radii with lengths of 5 5 , 4 4 , and 8 8 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?