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Question

Calculate packing fraction from the following figure to two decimal places.  Multiply it by 100 and enter the value.


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Solution

We know that packing fraction is the amount of space occupied in a unit cell. So, here the unit cell will be the square and the circle inside occupies some space.

P.F=Area occupied by circleArea of square

= (pi  r2)a2

 Notice that a = 2r 

 So, P.F = (pi  r2)(2r)2

             = (pi  r2)4r2

                   = pi4 = 0.78 

 0.78 100 = 78

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