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# Calculate packing fraction in the following case to two decimal places. All circles are of equal radius. Multiply the answer by 100 and enter the value. ___

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Solution

## It is quite similar to the previous question, just that you will have to join the three circles along the diagonal to get the relationship between r and a. We cannot use the circles along the side of the square since they are not touching each other. So, diagonal of square = r + 2r + r = 4r √2a = 4r So, P.F = Area occupied by circles inside square unit cellArea of the square unit cell But how to calculate area occupied by circles easily? Will it be 2 ∗ Area of one circle? Yes, because the circles at the corners contribute 14th of their area to the square. Since there are 4, we get 4 ∗14 = 1 And then there is one circle inside, so 1 + 1 = 2 Now, P.F = 2 ∗ (pi ∗ r2)a2 = 2 ∗ (pi ∗ r2)(2r2) = pi4=0.785 Notice that the P.F is same as that calculated in the previous question. What can you infer from that?  Suggest Corrections  0      Similar questions
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