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?

1 Answer
Jan 27, 2018

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

Explanation:

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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