An ellipsoid has radii with lengths of $6$ $6$ , $7$ $7$ , and $3$ $3$ . A portion the size of a hemisphere with a radius of $3$ $3$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-12T19:01:51

$= 471.3$ $=471.3$

The Volume of an Ellipsoid with radii $= 6, 7 and 3$ $=6,7 and 3$

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

$= \frac{π}{6} (2 \times 7) (2 \times 3) (2 \times 6)$ $=pi/6(2times7)(2times3)(2times6)$

$= \frac{π}{6} (14 \times 6 \times 12)$ $=pi/6(14times6times12)$

$= 168 π$ $=168pi$

$= 527.8$ $=527.8$

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

$= \frac{2}{3} π (27)$ $=2/3pi(27)$

$= 18 π$ $=18pi$

$= 56.5$ $=56.5$

So the remaining volume of the Ellipsoid

$= 527.8 - 56.5$ $=527.8-56.5$

$= 471.3$ $=471.3$

An ellipsoid has radii with lengths of 66 , 77 , and 33 . A portion the size of a hemisphere with a radius of 33 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?