An ellipsoid has radii with lengths of $9$ , $8$ , and $10$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-13T08:43:57

$=2754.2$

The Volume of an Ellipsoid with radii $=9,8 and 10$

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

$=pi/6(2times10)(2times8)(2times9)$

$=pi/6(20times16times18)$

$=960pi$

$=3016$

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

$=2/3pitimes125$

$=83.34pi$

$=261.8$

So the remaining volume of the Ellipsoid

$=3016-261.8$

$=2754.2$

An ellipsoid has radii with lengths of 9 9 , 8 8 , and 10 10 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?