An ellipsoid has radii with lengths of 6 , 9 , and 5 . 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?

1 Answer

216\pi\ \text{unit}^3

Explanation:

The volume V of ellipsoid of radii a=6, b=9 & c=5 is given as

V={4\pi}/3abc

={4\pi}/3(6)(9)(5)

=360\pi

The volume V_1 of hemisphere of radius r=6 is given as

V_1=1/2({4\pi}/3r^3)

={2\pi}/3r^3

={2\pi}/3(6)^3

=144\pi

hence the volume of ellipsoid after removing the volume of hemisphere

=V-V_1

=360\pi-144\pi

=216\pi\ \text{unit}^3