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

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