An ellipsoid has radii with lengths of $6$ , $4$ , and $8$ . A portion the size of a hemisphere with a radius of $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Question

1478 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-20T13:15:53

The remaining volume is $=787.49u^3$

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

Here,

$a=6u$

$b=4u$

and $c=8u$

so,

$V_e=4/3pixx6xx4xx8=576pi=804.25u^3$

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

Here,

$r=2u$

so,

$V_h=2/3pir^3=2/3pixx2^3=16.76u^3$

The remaining volume is

$V_r=V_e-V_h=804.25-16.76=787.49u^3$

An ellipsoid has radii with lengths of 6 6 , 4 4 , and 8 8 . A portion the size of a hemisphere with a radius of 2 2 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?