An ellipsoid has radii with lengths of $1$ , $3$ , and $2$ . 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?

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Answer 1 · 2018-07-22T07:00:09

The remaining volume is $=8.38u^3$

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,

$a=1$

$b=3$

$c=2$

$r=2$

The remaining volume is

$V_r=V_e-V_h$

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

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

$=2/3pi(2*1*3*2-2^3)$

$=2/3pi*(12-8)$

$=8/3pi$

$=8.38u^3$

An ellipsoid has radii with lengths of 1 1 , 3 3 , and 2 2 . 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?