An ellipsoid has radii with lengths of $6$ , $9$ , and $5$ . 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 · 2018-07-26T16:07:22

$216\pi\ \text{unit}^3$

The volume $V$ of ellipsoid of radii $a=6, b=9$ & $c=5$ is given as

$V={4\pi}/3abc$

$={4\pi}/3(6)(9)(5)$

$=360\pi$

The volume $V_1$ of hemisphere of radius $r=6$ is given as

$V_1=1/2({4\pi}/3r^3)$

$={2\pi}/3r^3$

$={2\pi}/3(6)^3$

$=144\pi$

hence the volume of ellipsoid after removing the volume of hemisphere

$=V-V_1$

$=360\pi-144\pi$

$=216\pi\ \text{unit}^3$

An ellipsoid has radii with lengths of 6 6 , 9 9 , and 5 5 . 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?