# 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?

##### 1 Answer

Nov 22, 2016

#### Explanation:

The ellipsoid has a volume of

#4/3 xx pi xx 4 xx 5 xx 7 = {560pi}/3#

The volume of the hemisphere is

#1/2 xx 4/3 xx pi xx 5^3 = {250pi}/3#

The volume remaining is

#{560pi}/3 - {250pi}/3 = {310pi}/3#