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.

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- Nov 29th 2010, 05:56 PMjpmath2010Pyramid 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.

- Nov 29th 2010, 08:01 PMSoroban
Hello, jpmath2010!

Quote:

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 $\displaystyle \sqrt{6}.$

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: .$\displaystyle 3 + \sqrt{6}$ units.

- Nov 30th 2010, 03:44 AMjpmath2010
Helo Soroban,

Thank you so much