An ellipsoid has radii with lengths of $8$ $8$ , $8$ $8$ , and $12$ $12$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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An ellipsoid has radii with lengths of $8$ $8$ , $8$ $8$ , and $12$ $12$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2018-07-20T01:42:41

$Remaining volume of ellipsoid V_{r} \approx 2764.6 cubic umits$ $color(purple)("Remaining volume of ellipsoid " V_r ~~ 2764.6 " cubic umits"$

Explanation:

$Vol. of ellipsoid = V_{e} = (\frac{4}{3}) π a \cdot b \cdot c$ $"Vol. of ellipsoid " = V_e = (4/3) pi a * b * c$

$If a = b = c, it becomes a sphere and vol. = V_{s} = (\frac{4}{3}) π r^{3}$ $"If a = b = c, it becomes a sphere and vol. " = V_s = (4/3) pi r^3$

$V o l . o f h e m i s p h e r e = V_{h} = \frac{V_{s}}{2} = (\frac{2}{3}) π r^{3}$ $"Vol. of hemisphere = V_h = V_s / 2 = (2/3) pi r^3$

$Given : a = 8, b = 8, c = 12, r = 6$ $"Given : " a = 8, b = 8, c = 12, r = 6$

$Remaining vol V_{r} = V_{e} - V_{h} = (\frac{4}{3}) π a^{2} c - (\frac{2}{3}) π r^{3}, a = b$ $"Remaining vol " V_r = V_e - V_h = (4/3) pi a^2 c - (2/3) pi r^3, a = b$

$V_{r} = (\frac{4}{3}) \cdot π \cdot 8^{2} \cdot 12 - (\frac{2}{3}) \cdot π \cdot 6^{3}$ $V_r = (4/3) * pi * 8^2 * 12 - (2/3) * pi * 6^3$

$Volume of remaining ellipsoid V_{r} \approx 2764.6 cubic umits$ $color(purple)("Volume of remaining ellipsoid " V_r ~~ 2764.6 " cubic umits"$

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An ellipsoid has radii with lengths of $8$ $8$ , $8$ $8$ , and $12$ $12$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Explanation:

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An ellipsoid has radii with lengths of $8$ $8$ , $8$ $8$ , and $12$ $12$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?