An ellipsoid has radii with lengths of $12$ $12$ , $16$ $16$ , and $8$ $8$ . A portion the size of a hemisphere with a radius of $8$ $8$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-13T12:47:01

$= 5361.67$ $=5361.67$

The Volume of an Ellipsoid with radii $= 12, 16 and 8$ $=12,16 and 8$

$= \frac{π}{6} \times$ $=pi/6times$ (major-axis) $\times$ $times$ (minor axis) $\times$ $times$ (vertcal-axis)

$= \frac{π}{6} (2 \times 16) (2 \times 8) (2 \times 12)$ $=pi/6(2times16)(2times8)(2times12)$

$= \frac{π}{6} (32 \times 16 \times 24)$ $=pi/6(32times16times24)$

$= 2048 π$ $=2048pi$

$= 6434$ $=6434$

Volume of an Hemisphere $= \frac{2}{3} (π r^{3})$ $=2/3(pir^3)$ where $r = 8$ $r=8$ is the radius
$= \frac{2}{3} π {(8)}^{3}$ $=2/3pi(8)^3$

$= \frac{2}{3} π \times 512$ $=2/3pitimes512$

$= 341.34 π$ $=341.34pi$

$= 1072.34$ $=1072.34$

So the remaining volume of the Ellipsoid

$= 6434 - 1072.34$ $=6434-1072.34$

$= 5361.67$ $=5361.67$

An ellipsoid has radii with lengths of 12 1212 , 16 1616 , and 8 88 . A portion the size of a hemisphere with a radius of 8 88 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?