An ellipsoid has radii with lengths of $9$ $9$ , $8$ $8$ , and $10$ $10$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-13T08:43:57

$= 2754.2$ $=2754.2$

The Volume of an Ellipsoid with radii $= 9, 8 and 10$ $=9,8 and 10$

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

$= \frac{π}{6} (2 \times 10) (2 \times 8) (2 \times 9)$ $=pi/6(2times10)(2times8)(2times9)$

$= \frac{π}{6} (20 \times 16 \times 18)$ $=pi/6(20times16times18)$

$= 960 π$ $=960pi$

$= 3016$ $=3016$

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

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

$= 83.34 π$ $=83.34pi$

$= 261.8$ $=261.8$

So the remaining volume of the Ellipsoid

$= 3016 - 261.8$ $=3016-261.8$

$= 2754.2$ $=2754.2$

An ellipsoid has radii with lengths of 9 99 , 8 88 , and 10 1010 . A portion the size of a hemisphere with a radius of 5 55 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?