Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?

The answer is 3+ root 69/3.

I really can't think of an approach, yet...

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- Jun 12th 2011, 10:29 PMVeronica1999spheres
Three mutually tangent spheres of radius 1 rest on a horizontal plane. A sphere of radius 2 rests on them. What is the distance from the plane to the top of the larger sphere?

The answer is 3+ root 69/3.

I really can't think of an approach, yet... - Jun 12th 2011, 10:32 PMProve It
The larger sphere would never be able to rest on two smaller spheres without falling... This question = FAIL!

- Jun 12th 2011, 11:14 PMearboth
1. The centers of the smaller spheres form a isosceles triangle with the side-length 2.

2. The center M of the larger sphere is vertically above the centroid F of the isosceles triangle. The larger sphere is tangent to all three smaller spheres.

3. is a right triangle with

hypotenuse

horizontal leg

vertical leg

4. You have to add one small radius and one large radius to the distance and you'll get the given result.

5. For additional information have a look here: Close-packing of spheres - Wikipedia, the free encyclopedia - Jun 12th 2011, 11:21 PMabhishekkgp
- Jun 13th 2011, 12:34 AMProve It
- Jun 13th 2011, 08:47 AMVeronica1999
Thank you so much Earboth!

- Jun 13th 2011, 02:13 PMbjhopperRe: spheres
also see Earboths solution of a four ball pile 12/22.10

- Jun 13th 2011, 06:08 PMVeronica1999Re: spheres
Thanks for the info. I really appreciate it.