Packing Circles

A 10x10 square can obviously hold 100 unit circles (diameter=1) when arranged
in rows and columns. How many additional circles can it hold if the circles
are packed closer, in a hexagonal arrangement?

What are the dimensions of the smallest area rectangle which can hold an
additional 10 unit circles when the arrangement changes from rows and columns
to hexagonal?

What are the dimensions of the smallest area rectangle which can hold
100 unit circles in a hexagonal arrangement?
Source: Original.
Solution
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