Shown is a 3-D unit cell pattern for a structure of packed spheres. The center o

Question

Shown is a 3-D unit cell pattern for a structure of packed spheres. The center of each of eight spheres is at a corner of the cube, and the part of each sphere 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 could be constructed?

Shown is a 3-D unit cell pattern for a structure of packed spheres. The center of each of eight spheres is at a corner of the cube, and the part of each sphere 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 could be constructed?

Explanation / Answer

as the centre of the sphere lies on the corners of the cube,

and we know there are 8 corners of a cube,

as we can see at the corners the spherical part is 1/4 th of a hemisphere = 1/8th of a sphere

so total = 8 corners * 1/8 of the sphere = 8*1/8 = 1 sphere

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