# An ellipsoid has radii with lengths of 6 , 5 , and 3 . A portion the size of a hemisphere with a radius of 6  is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Aug 16, 2016

Since the volume of the Volume of the Hemisphere is larger than the volume of the Ellipsoid.
Therefore it is not possible to remove the Hemisphere of the size given$\left(r = 6\right)$

#### Explanation:

The Volume of an Ellipsoid with radii $= 6 , 5 \mathmr{and} 3$

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

$= \frac{\pi}{6} \left(2 \times 6\right) \left(2 \times 3\right) \left(2 \times 5\right)$

$= \frac{\pi}{6} \left(12 \times 6 \times 10\right)$

$= 120 \pi$

$= 377$

Volume of an Hemisphere$= \frac{2}{3} \left(\pi {r}^{3}\right)$ where $r = 6$ is the radius
$= \frac{2}{3} \pi {\left(6\right)}^{3}$

$= \frac{2}{3} \pi \times 216$

$= 144 \pi$

$= 452.4$

Since the volume of the Volume of the Hemisphere is larger than the volume of the Ellipsoid.
Therefore it is not possible to remove the Hemisphere of the size given$\left(r = 6\right)$