Consider the arrangement of circles of equal radii with their centres arranged as per the 2-dimensional lattice defined by $a = b, θ = 60 °$ such that each circle is touching all its nearest neighbours. If all the void areas present are additionally occupied by smaller circles of relevant size so that the void circles are just contacting their neighbours. Find the packing efficiency of the configuration in percent. (Give your answer as 100 – value)

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Detailed Solution

Packing fraction $= \frac{\frac{1}{2} π R^{2} + π 0.155 R^{2}}{\frac{1}{2} 2 R^{2} \frac{\sqrt{3}}{2}}$

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