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

1 Answer
Aug 7, 2018

The volume remaining is =320.4u^3

Explanation:

The volume of an ellipsoid is

V_e=4/3piabc

The volume of a hemisphere is

V_h=1/2*4/3pir^3=2/3pir^3

Here,

a=3

b=6

c=5

r=3

The remaining volume is

V_r=V_e-V_h

=4/3piabc-2/3pir^3

=2/3pi(2abc-r^3)

=2/3pi(2*3*6*5-3^3)

=2/3pi*(180-27)

=(2*153)/3pi

=320.4u^3