If the circle segments enclosed inside each of the bold-faced parallelograms sho

Question

If the circle segments enclosed inside each of the bold-faced parallelograms shown here were cut out and taped together, how many whole circles could be constructed for each one of the patterns? Shown at the right is a three-dimensional unit cell pattern for a structure of equalsized packed spheres. The center of each of eight spheres is at a comer of the cube, and the part of each that lies within the boundaries of the cube is shown. If all of the sphere segments enclosed inside the unit cell boundaries could be glued together, how many whole spheres would be constructed If a smaller sphere were placed in the center of this unit cell pattern, what would its coordination number be?

Explanation / Answer

C) #6 Two circles can be constructed. One full circle and another made from 4 equivalent sector of four circles.

#7 One circle can be constructed by 4 sector cut out

#8 One circle can be constructed by 4 different sector cut out from the parallelogram.

D) One sphere can be made.

There are 8 corners of the cube and each sphere at corner is contributing 1/8th of its part and there total eight corners and one sphere at each corner.

Therefore No. of sphere =8 x 1/8 = 1

On placing a smaller sphere at centre

No of sphere will become two and its coordination number is 8

Coordination number is thr number of circle touching the central circle. In this 8 circle at the corner are touching the circle at the corner.

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