Question

Spherical balls of radius r are arranged in a
lattice structure as an imaginary ube. 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?​

Answer 1

Given: Radius of the spherical ball = r

A sphere at vertex of cube and centre of cube

To Find : Distance between the centers of the spheres on two adjacent vertices.

Solution :

Let the imaginary cube be as small as possible.

Let the length of the edge of cube be = a

Let the radius of sphere be = r

Now,

Sphere present at the vertex will contribute 1/8th part in volume, whereas the sphere at centre will contribute whole part.

Radius of the sphere will occupy 1/2 of the edge length.

Therefore,

Edge length, a = 2r

Answer : Distance between centers of spheres on two adjacent vertices is 2r