An ellipsoid has radii with lengths of $5$ $5$ , $4$ $4$ , and $8$ $8$ . 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 · 2016-08-14T18:22:18

$= 613.65$ $=613.65$

The Volume of an Ellipsoid with radii $= 5, 4 and 8$ $=5,4 and 8$

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

$= \frac{π}{6} (2 \times 8) (2 \times 4) (2 \times 5)$ $=pi/6(2times8)(2times4)(2times5)$

$= \frac{π}{6} (16 \times 8 \times 10)$ $=pi/6(16times8times10)$

$= \frac{640 π}{3}$ $=(640pi)/3$

$= 670.2$ $=670.2$

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

$= \frac{2}{3} π \times 27$ $=2/3pitimes27$

$= 18 π$ $=18pi$

$= 56.55$ $=56.55$

So the remaining volume of the Ellipsoid

$= 670.2 - 56.55$ $=670.2-56.55$

$= 613.65$ $=613.65$

An ellipsoid has radii with lengths of 55 , 44 , and 88 . 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?