Question

Spherical balls of radius r are arranged in a lattice structure as an imaginary cube. There is a
sphere at each vertex of the cube and one sphere at the centre of the cube, If this imaginary
cube is to be as small as possible, then what is the distance between the centers of the spheres
on two adjacent vertices?

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Answer 1

The distance between the centers of the spheres

on two adjacent vertices is :

• We have considered this imaginary cube as small as possible.

Let the edge length of cube be a and radius of sphere be r

• We are given that sphere is placed at each vertices of the cube and one whole sphere is placed in the centre of the cube.

• The sphere present at the vertex contribute 1/8th part of it in volume and sphere at centre contribute whole part.

• We can see from the daigram that, radius of sphere is occupying 1/2 of the edge length.

Hence, we can say that

Edge length, a = 2r

• The distance between the centers of the spheres on two adjacent vertices is 2r or a