An ellipsoid has radii with lengths of #14 #, #7 #, and #6 #. A portion the size of a hemisphere with a radius of #9 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2018-01-27T09:45:24

#color(green)(V_r = color(green)(936.5714)# cubic units

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Ellipsoid volume #V_e = (4/3) pi a b c#

Given : #a = 14, b= 7, c = 6#

#color(blue)(V_e) = (4/3) pi (14*7*6) = color(blue)(2464)# cubic units

Volume of hemi sphere #V_h = (2/3) pi r^3#

Given #r = 9#

#color(blue)(V_h) = (2/3) pi 9^3 = color(blue)(1527.4286)# cubic units

Remaining volume of ellipsoid

#color(green)(V_r =2464 - 1527.4286 = color(green)(936.5714)# cubic units