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?

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Answer 1 · 2018-01-27T09:21:59

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

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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)#