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

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: . units.