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?

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Answer 1 · 2018-08-07T08:50:13

The volume remaining is $=320.4u^3$

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,

$a=3$

$b=6$

$c=5$

$r=3$

The remaining volume is

$V_r=V_e-V_h$

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

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

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

$=2/3pi*(180-27)$

$=(2*153)/3pi$

$=320.4u^3$

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