An ellipsoid has radii with lengths of $6$ , $5$ , and $3$ . 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?

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Answer 1 · 2016-08-12T19:06:57

$=375$

The Volume of an Ellipsoid with radii $=6,5 and 3$

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

$=pi/6(2times6)(2times3)(2times5)$

$=pi/6(12times6times10)$

$=120pi$

$=377$

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

$=2/3pi$

$=2$

So the remaining volume of the Ellipsoid

$=377-2$

$=375$

An ellipsoid has radii with lengths of 6 6 , 5 5 , and 3 3 . 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?