An ellipsoid has radii with lengths of $5$ , $6$ , and $7$ . A portion the size of a hemisphere with a radius of $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-19T18:27:22

The remaining volume is $=(590pi)/3$

The volume of an ellipsoid is $=(4piabc)/3$

The volume of a hemisphere is $=(2pir^3)/3$

The remaining volume is $=(4piabc)/3-(2pir^3)/3$

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

Here,

$a=5$

$b=6$

$c=7$

$r=5$

Therefore, the remaining volume is

$=((2pi)/3)(2*5*6*7-5^3)$

$=(10pi)/3(84-25)$

$=(590pi)/3$

An ellipsoid has radii with lengths of 5 5 , 6 6 , and 7 7 . A portion the size of a hemisphere with a radius of 5 5 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?