An ellipsoid has radii with lengths of $6$ , $7$ , and $6$ . 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

1307 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-09T23:09:48

The remaining volume is:
$V_r ~~ 794" units"^3$

$V = 4/3piabc$ where a, b, and c are the radii.

$V = 4/3pi(6)(7)(6)$

$V = 4/3pir^3$

The volume of the hemisphere is half of that:

$V = 4/6pi5^3$

The remaining volume is the difference:

$V_r = 4/3pi(6(7)(6) - 5^3/2)$

$V_r ~~ 794" units"^3$

An ellipsoid has radii with lengths of 6 6 , 7 7 , and 6 6 . 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?