# An ellipsoid has radii with lengths of 2 , 4 , and 5 . A portion the size of a hemisphere with a radius of 2  is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Aug 9, 2016

$= 150.8$

#### Explanation:

The Volume of an Ellipsoid with radii $= 2 , 4 \mathmr{and} 5$
$= \frac{\pi}{6} \times$(major-axis)$\times$(minor axis)$\times$(vertcal-axis)
$= \frac{\pi}{6} \left(2 \times 2\right) \left(2 \times 4\right) \left(2 \times 5\right)$
$= \frac{\pi}{6} \left(4 \times 8 \times 10\right)$
$= 53.33 \pi$
$= 167.55$
Volume of an Hemisphere$= \frac{2}{3} \left(\pi {r}^{3}\right)$ where $r = 2$ is the radius
$= \frac{2}{3} \pi {\left(2\right)}^{3}$
$= \frac{2}{3} \pi \left(8\right)$
$= \frac{16}{3} \pi$
$= 16.75$
So the remaining volume of the Ellipsoid
$= 167.55 - 16.75$
$= 150.8$