00:01
Fill the room with tennis balls and calculate the amount of balls which this room can accommodate so this this task is not as simple as it seems to be obviously in order to feel the room with the boss without balls being crushed we have to follow the following condition so total volume of the balls should be below the volume of the room but obviously we cannot feel all the empty space with the ball because for example, let's imagine a table and we fill this table with the balls.
00:40
Even if we put it as dense as we can, the number of the part of the volume occupied by the balls will be below the volume, the available volume.
01:00
And the overall volume which is provided by this, let's say small box, equals to the volume which is occupied by the balls plus volume of the space, which is unoccupied.
01:23
And therefore, we have to make a correction with respect to this unoccupied space.
01:29
To accommodate as many balls as we can in a cubic room, we are going to apply cubic clothes packing, which comes from the crystal structure of the solids.
01:45
This is also called abc packing.
01:56
It means that each third layer resembles the previous third layer.
02:05
And this packing has highest pecking efficiency, which is roughly 74 .05%.
02:20
So it means that the total volume, which can be occupied by both, equals to this efficiency, multiply by volume of the room, and divided by 100 % obviously.
02:40
Let's calculate this maximum volume.
02:45
So it equals to 74 .05 divided by 100, and multiply by the volume of the room, which is 4 by 4 by 3 cubic meters.
02:59
So let's calculate this number...