>>11418837Let's say you have a r meters cube of cheese and inside it you have a r/3 meters radius sphere whose center coincides with that of the cube.
What is the volume of leftover cheese?
=r^3 - 4/3*pi*(r/3)^3
Let's say this value is V
Therefore
V=r^3 - 4/3*pi*(r/3)^3
Now let's have k more such blocks of cheese as stated by your second condition. What is the total left over volume?
V'=(r^3 - 4/3*pi*(r/3)^3)+(r^3 - 4/3*pi*(r/3)^3)+(r^3 - 4/3*pi*(r/3)^3)......k times
V'=k*(r^3 - 4/3*pi*(r/3)^3)
V'=k*V
Hence k>1
We can also say that we now have k holes. But since the volume of holes is always less than the volume of the cube, your third and final statements are both wrong.
