An ellipsoid has radii with lengths of $9$ , $4$ , and $8$ . A portion the size of a hemisphere with a radius of $3$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-12-05T10:41:29

The remaining volume is $=1149.9u^3$

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

Here,

$a=9u$

$b=4u$

and $c=8u$

so,

$V_e=4/3pixx9xx4xx8=384pi=1206.4u^3$

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

$V_r=V_e-V_h=1206.4-56.5=1149.9u^3$

An ellipsoid has radii with lengths of 9 9 , 4 4 , and 8 8 . A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?