An ellipsoid has radii with lengths of $5$ , $12$ , and $7$ . A portion the size of a hemisphere with a radius of $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-16T12:55:16

$=1307$

The Volume of an Ellipsoid with radii $=5,12 and 7$

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

$=pi/6(2times12)(2times5)(2times7)$

$=pi/6(24times10times14)$

$=560pi$

$=1759.3$

Volume of an Hemisphere $=2/3(pir^3)$ where $r=6$ is the radius
$=2/3pi(6)^3$

$=2/3pitimes216$

$=144pi$

$=452.4$

So the remaining volume of the Ellipsoid

$=1759.3-452.4$

$=1307$

An ellipsoid has radii with lengths of 5 5 , 12 12 , and 7 7 . A portion the size of a hemisphere with a radius of 6 6 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?