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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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!
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.
Helo Soroban,
Thank you so much
