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February 18th, 2019, 02:02 PM   #1
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Fitting spheres in cylinder

If a cylinder has diameter 6 cm and a number of identical of spheres have diameter of 2 cm, how many spheres can fit into a layer at the bottom of the cylinder?

For this question I got 5, forming a cross shape using the diameter of the cylinder. But I'm not sure how to prove this.

A second layer is added, where each sphere is touching 3 spheres in the first layer. How far apart are the centres of these 3 marbles?

Here I'm not sure how to visualize the position of the spheres...

Finally, one last sphere is added as a third layer. What is the length between the base of the cylinder and the top of this last sphere?

(hint: cos(30) = √3/2)
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