An ellipsoid has radii with lengths of $6$ , $11$ , and $8$ . A portion the size of a hemisphere with a radius of $8$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Question

1343 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-27T09:21:59

Remaining volume of ellipsoid $color(green)(V_r) ~~ color(green)(1138.9193)$

enter image source here

Volume of Ellipsoid $V_e = (4/3) pi a b c$

volume of hemisphere $V_h = (2/3) pi r^3$

Given : $a = 6, b = 11, c = r = 8$

$color(purple)(V_e) = (4/3) pi * 6 * 11 * 8 ~~ color(purple)(2211.6812)$

$color(purple)(V_h) = (2/3) * pi * (8)^3 ~~ color(purple)(1072.7619)$

Remaining volume of ellipsoid $color(green)(V_r) = V_e - V_h = 2211.6812 - 1072.7619 ~~ color(green)(1138.9193)$

An ellipsoid has radii with lengths of 6 6 , 11 11 , and 8 8 . A portion the size of a hemisphere with a radius of 8 8 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?