volume of cylinders and freespace

dogleg

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A one litre cylinder has a diameter equal to its height. A ball fits exactly into this cylinder. What is the maximum diameter of each ball of a ring of balls that would fit into the free space at the top and bottom of the cylinder? Assume a closed cylinder.
 
A one litre cylinder has a diameter equal to its height. A ball fits exactly into this cylinder. What is the maximum diameter of each ball of a ring of balls that would fit into the free space at the top and bottom of the cylinder? Assume a closed cylinder.

Great problem! Draw a sketch first and ponder the geometry! So what are your thoughts?

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