An ellipsoid has radii with lengths of $8$ , $8$ , and $12$ . A portion the size of a hemisphere with a radius of $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2018-07-20T01:42:41

$color(purple)("Remaining volume of ellipsoid " V_r ~~ 2764.6 " cubic umits"$

$"Vol. of ellipsoid " = V_e = (4/3) pi a * b * c$

$"If a = b = c, it becomes a sphere and vol. " = V_s = (4/3) pi r^3$

$"Vol. of hemisphere = V_h = V_s / 2 = (2/3) pi r^3$

$"Given : " a = 8, b = 8, c = 12, r = 6$

$"Remaining vol " V_r = V_e - V_h = (4/3) pi a^2 c - (2/3) pi r^3, a = b$

$V_r = (4/3) * pi * 8^2 * 12 - (2/3) * pi * 6^3$

$color(purple)("Volume of remaining ellipsoid " V_r ~~ 2764.6 " cubic umits"$

An ellipsoid has radii with lengths of 8 8 , 8 8 , and 12 12 . A portion the size of a hemisphere with a radius of 6 6 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?