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?

1 Answer
sankarankalyanam
Jan 27, 2018

Remaining volume of ellipsoid color(green)(V_r) ~~ color(green)(1138.9193)Vr≈1138.9193

Explanation:

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Volume of Ellipsoid V_e = (4/3) pi a b cVe=(43)πabc

volume of hemisphere V_h = (2/3) pi r^3Vh=(23)πr3

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

color(purple)(V_e) = (4/3) pi * 6 * 11 * 8 ~~ color(purple)(2211.6812)Ve=(43)π⋅6⋅11⋅8≈2211.6812

color(purple)(V_h) = (2/3) * pi * (8)^3 ~~ color(purple)(1072.7619)Vh=(23)⋅π⋅(8)3≈1072.7619

Remaining volume of ellipsoid color(green)(V_r) = V_e - V_h = 2211.6812 - 1072.7619 ~~ color(green)(1138.9193)Vr=Ve−Vh=2211.6812−1072.7619≈1138.9193

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