An ellipsoid has radii with lengths of $3$ $3$ , $6$ $6$ , and $5$ $5$ . A portion the size of a hemisphere with a radius of $2$ $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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An ellipsoid has radii with lengths of $3$ $3$ , $6$ $6$ , and $5$ $5$ . A portion the size of a hemisphere with a radius of $2$ $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2018-08-09T17:33:18

$\frac{340}{3} π \approx 356 {units}^{3}$ $340/3pi~~356" units"^3$

Explanation:

$the volume of the ellipsoid is$ $"the volume of the ellipsoid is"$

$∙ x V_{ellipsoid} = \frac{4}{3} π r_{1} r_{2} r_{3}$ $•color(white)(x)V_(color(red)"ellipsoid")=4/3pir_1r_2r_3$

$V_{ellipsoid} = \frac{4}{3} π \times 3 \times 6 \times 5 = 120 π$ $V_("ellipsoid")=4/3pixx3xx6xx5=120pi$

$the volume of the hemisphere is$ $"the volume of the hemisphere is"$

$∙ x V_{hemisphere} = \frac{2}{3} π r^{3}$ $•color(white)(x)V_(color(red)"hemisphere")=2/3pir^3$

$V_{hemisphere} = \frac{2}{3} π \times 8 = \frac{16}{3} π$ $V_("hemisphere")=2/3pixx8=16/3pi$

$V_{remaining} = 120 π - \frac{16}{3} π = \frac{340}{3} π \approx 356 {units}^{3}$ $V_("remaining")=120pi-16/3pi=340/3pi~~356" units"^3$

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An ellipsoid has radii with lengths of $3$ $3$ , $6$ $6$ , and $5$ $5$ . A portion the size of a hemisphere with a radius of $2$ $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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An ellipsoid has radii with lengths of $3$ $3$ , $6$ $6$ , and $5$ $5$ . A portion the size of a hemisphere with a radius of $2$ $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?