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

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

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Answer 1 · 2018-08-09T17:33:18

$340/3pi~~356" units"^3$

Explanation:

$"the volume of the ellipsoid is"$

$•color(white)(x)V_(color(red)"ellipsoid")=4/3pir_1r_2r_3$

$V_("ellipsoid")=4/3pixx3xx6xx5=120pi$

$"the volume of the hemisphere is"$

$•color(white)(x)V_(color(red)"hemisphere")=2/3pir^3$

$V_("hemisphere")=2/3pixx8=16/3pi$

$V_("remaining")=120pi-16/3pi=340/3pi~~356" units"^3$

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

1 Answer

Explanation:

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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?

1 Answer

Explanation:

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