An ellipsoid has radii with lengths of $2$ $2$ , $7$ $7$ , and $4$ $4$ . 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 · 2016-08-11T22:06:32

$≅ 178$ $~=178$

The Volume of an Ellipsoid with radii $= 2, 7 and 4$ $=2,7 and 4$

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

$= \frac{π}{6} (2 \times 7) (2 \times 2) (2 \times 4)$ $=pi/6(2times7)(2times2)(2times4)$

$= \frac{π}{6} (14 \times 4 \times 8)$ $=pi/6(14times4times8)$

$= 74.67 π$ $=74.67pi$

$= 234.57$ $=234.57$

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

$= 234.57 - 56.5$ $=234.57-56.5$

$≅ 178$ $~=178$

An ellipsoid has radii with lengths of 2 22 , 7 77 , and 4 44 . A portion the size of a hemisphere with a radius of 3 33 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?