Question

1.42875 balls of stones have been kept in a box in the form of a cube. How many layers of balls are there in the box?​

Answer 1

Answer:

Experiment shows that dropping the spheres in randomly will achieve a density of around 65%. However, a higher density can be achieved by carefully arranging the spheres as follows. Start with a layer of spheres in a hexagonal lattice, then put the next layer of spheres in the lowest points you can find above the first layer, and so on – this is just the way you see oranges stacked in a shop. At each step there are two choices of where to put the next layer, so this natural method of stacking the spheres creates an uncountably infinite number of equally dense packings, the best known of which are called cubic close packing and hexagonal close packing. Each of these arrangements has an average density of π32√=0.740480489.... The Kepler conjecture says that this is the best that can be done—no other arrangement of spheres has a higher average density.

Answer 2

Answer:

35 layers are there...

Step-by-step explanation:

balls in the box= 42875

layers of balls= ?

volume of cube= (side)^⅓

42875 = (side)^⅓

side = ^⅓√42875

= 35 layers.