An ellipsoid has radii with lengths of 8 , 4 , and 7 . 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 3, 2017

The remaining volume is =881.8u^3

Explanation:

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

Here,

a=8u

b=4u

and c=7u

so,

V_e=4/3pixx8xx4xx7=1920pi=938.3u^3

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

Here,

r=7u

so,

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

The remaining volume is

V_r=V_e-V_h=938.3-56.5=881.8u^3