An ellipsoid has radii with lengths of $6$ , $9$ , and $4$ . 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?

Question

1240 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-10T20:10:39

The remaining volume is: $V =614/3pi$

I will give this reference for the Volume of an Ellipsoid

$V = 4/3piabc$

We are given $a = 6$ , $b = 9$ , and $c = 4$ :

$V = 288pi$

I will give this reference for the Volume of a sphere

$V = 4/3pir^3$

For hemisphere, we must divide by 2:

$V = 4/6pir^3$

We are given $r = 5$ :

$V = 250/3pi$

The remaining volume is the difference:

$V =614/3pi$

An ellipsoid has radii with lengths of 6 6 , 9 9 , and 4 4 . 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?