Clear explanation of karma-kun's answer to the final math problem in Assassination Classroom? I've been trying to understand Karma-kun's answer the math problem in the Examination Finals.

I have searched references, and explanations to the problem but to no avail. I still couldn't understand the horrible explanations to the problem, and the answer assumes that you know their thought process is, which I don't. 

This has an english translation of the problem:

young-il-long-kiyoshi.tumblr.com/post/125623681248/on-the-topic-of-the-final-maths-question-in-the



Another link I found mentioning the problem but not explaining it.

angryanimebitches.com/2016/03/assassination-classroom-season-2-episode-12-the-principal-is-a-sore-loser/



Their is also a youtube video that explains Karma-kun's answer but even his explanation I still can't understand how he to the conclusion that the area of the center atom is equal to the half the area of the cube divided by two. a^3/2

video link: Weird Geometry (Assassination Classroom S2 E12)



The reason I'm posting this is that there is no other way for me to understand the problem without asking in a thread.

I just want an explanation of the answer in "high-school" level of perspective, not a professional PhD level one...

I don't want to hear "equidistant", "inifinitesimal", "vertex" or any other technical terms that I can't comprehend.

I know I demand too much, but please help me understand how Karma-kun got a^3/2. The only perspective that I got from Karma is that all the 8 atoms form a cube of their own, and the middle point of that imaginary cube is equivalent to all the atoms inside the 8 individual cubes.

And the video says so as well, but how the in the world has it gone from A 1/8 to 2A? and then a^3/2

as shown here:
All the atoms in the crystal lattice are identical. Let's say the volume of an atom at the vertex (not corner, if it is a corner, you will need a slightly different reasoning) is B. Each atom at the vertex takes up (1/8)B of the cube.  See diagram.



For a cube with length a, it consists of the central atom A with volume D and  8 atoms at the vertices each taking up (1/8)B of the cube. Thus,

a3 = D + 8 × (1/8)B

However, since we  know that the atoms at the vertices are actually identical to the central atom, The volume B is equal to D and hence,

a3 = B + 8 × (1/8)B ==> B = (1/2)a3

QED

All the technical terms that you have mentioned are what I was learning in my high school. This question is not hard, as Karma has said. It is a combined question of maths and chemistry.