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Math Help - Pyramid of spheres.

  1. #1
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    Pyramid of spheres.

    four sphere, each of radius 1.5, are placed in a pile with three at the base and the other on top. If each sphere touches the other three spheres, give the height of the pile.
    Last edited by mr fantastic; November 30th 2010 at 12:29 AM. Reason: Re-titled.
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  2. #2
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    Hello, jpmath2010!

    Four spheres, each of radius 1.5, are placed in a pile with 3 at the base and 1 on top.
    If each sphere touches the other three spheres, give the height of the pile.

    We have a "pyramid" of spheres.

    The centers of the spheres form a regular tetrahedron of side 3.
    . . The height of the tetrahedron is \sqrt{6}.

    The tetrahedron lies 1.5 units above the bottom of the pyramid
    . . and 1.5 units below the top of the pyramid.

    The height of the pyramid is: . 3 + \sqrt{6} units.

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  3. #3
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    Helo Soroban,

    Thank you so much
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