An ellipsoid has radii with lengths of $14$ , $11$ , and $7$ . A portion the size of a hemisphere with a radius of $9$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2018-07-27T09:26:02

$2988.702\ \text{unit}^3$

The volume $V$ of ellipsoid of radii $a=14, b=11$ & $c=7$ is given as

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

$={4\pi}/3(14)(11)(7)$

$={4312\pi}/3$

The volume $V_1$ of hemisphere of radius $r=9$ is given as

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

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

$={2\pi}/3(9)^3$

$=486\pi$

hence the volume of ellipsoid after removing the volume of hemisphere

$=V-V_1$

$={4312\pi}/3-486\pi$

$={2854\pi}/3$

$=2988.702\ \text{unit}^3$

An ellipsoid has radii with lengths of 14 14 , 11 11 , and 7 7 . A portion the size of a hemisphere with a radius of 9 9 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?