# An ellipsoid has radii with lengths of 4 , 5 , and 7 . A portion the size of a hemisphere with a radius of 5  is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Nov 22, 2016

$\frac{310 \pi}{3}$

#### Explanation:

The ellipsoid has a volume of

$\frac{4}{3} \times \pi \times 4 \times 5 \times 7 = \frac{560 \pi}{3}$

The volume of the hemisphere is

$\frac{1}{2} \times \frac{4}{3} \times \pi \times {5}^{3} = \frac{250 \pi}{3}$

The volume remaining is

$\frac{560 \pi}{3} - \frac{250 \pi}{3} = \frac{310 \pi}{3}$