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.
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.
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 $\displaystyle \sqrt{6}.$
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.