An ellipsoid has radii with lengths of $4$ $4$ , $9$ $9$ , and $5$ $5$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2016-08-14T16:11:59

$= 492.2$ $=492.2$

The Volume of an Ellipsoid with radii $= 4, 9 and 5$ $=4,9 and 5$

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

$= \frac{π}{6} (2 \times 9) (2 \times 4) (2 \times 5)$ $=pi/6(2times9)(2times4)(2times5)$

$= \frac{π}{6} (18 \times 8 \times 10)$ $=pi/6(18times8times10)$

$= 240 π$ $=240pi$

$= 754$ $=754$

Volume of an Hemisphere $= \frac{2}{3} (π r^{3})$ $=2/3(pir^3)$ where $r = 5$ $r=5$ is the radius
$= \frac{2}{3} π {(5)}^{3}$ $=2/3pi(5)^3$

$= \frac{2}{3} π \times 125$ $=2/3pitimes125$

$= \frac{250 π}{3}$ $=(250pi)/3$

$= 261.8$ $=261.8$

So the remaining volume of the Ellipsoid

$= 754 - 261.8$ $=754-261.8$

$= 492.2$ $=492.2$

An ellipsoid has radii with lengths of 44 , 99 , and 55 . A portion the size of a hemisphere with a radius of 55 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?