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Thread: Sphere Problem (Solid Mensuration)

  1. #1
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    Sphere Problem (Solid Mensuration)

    Hello, good day to all! Please, I need your help about this problem. Thanks. ☺

    Each of the twelve edges of a cube of edge a is tangent to a sphere. Find the volume of that portion of the cube which lies outside the sphere.
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  2. #2
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    Re: Sphere Problem (Solid Mensuration)

    Attached is the best visual I could steal (ignore the red octahedron) ...

    in terms of the sphere radius, $R$, the volume within the cube and outside the sphere ...

    $V = R^3\bigg[2\sqrt{2}-\dfrac{\pi}{6}(15\sqrt{2}-16) \bigg]$
    Attached Thumbnails Attached Thumbnails Sphere Problem (Solid Mensuration)-59aac98d-c46d-429f-9c86-d71b5b4af19e-198-00000021dd608021_tmp.png  
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