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?

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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?

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Answer 1 · 2018-01-27T09:21:59

Remaining volume of ellipsoid $V_{r} \approx 1138.9193$ $color(green)(V_r) ~~ color(green)(1138.9193)$

Explanation:

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Volume of Ellipsoid $V_{e} = (\frac{4}{3}) π a b c$ $V_e = (4/3) pi a b c$

volume of hemisphere $V_{h} = (\frac{2}{3}) π r^{3}$ $V_h = (2/3) pi r^3$

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

$V_{e} = (\frac{4}{3}) π \cdot 6 \cdot 11 \cdot 8 \approx 2211.6812$ $color(purple)(V_e) = (4/3) pi * 6 * 11 * 8 ~~ color(purple)(2211.6812)$

$V_{h} = (\frac{2}{3}) \cdot π \cdot {(8)}^{3} \approx 1072.7619$ $color(purple)(V_h) = (2/3) * pi * (8)^3 ~~ color(purple)(1072.7619)$

Remaining volume of ellipsoid $V_{r} = V_{e} - V_{h} = 2211.6812 - 1072.7619 \approx 1138.9193$ $color(green)(V_r) = V_e - V_h = 2211.6812 - 1072.7619 ~~ color(green)(1138.9193)$

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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?

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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?