An ellipsoid has radii with lengths of 9 , 8 , and 6 . 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
Dec 6, 2017

The remaining volume is =1753.1u^3

Explanation:

The volume of an ellipsoid is V_e=4/3abc where a, b, and c are the lengths.

Here,

a=9u

b=8u

and c=6u

so,

V_e=4/3pixx9xx8xx6=576pi=1809.6u^3

The volume of a hemisphere is V_h=2/3pir^3 where r is rhe radius

Here,

r=3u

so,

V_h=2/3pir^3=2/3pixx3^3=56.5u^3

The remaining volume is

V_r=V_e-V_h=1809.6-56.5=1753.1u^3