Mathematical brains required - the space between 4 spheres

[D D Danneh]

How did you work this out? I cant get my head around it

I modelled it in 3D and took a volume of it. Which is why I said it's a crude method, because I can't guarantee it took the correct measurement of it. However, dividing the overall area of the sphere by the given volume gave me 23.9998, which I reckon is close enough to 24 to say it's probably 1/24.

I thought I was on to something when I realised you could create an icosahedron from equilateral triangles (like the one which is created from the 3 points of the radius of the sphere), but it was not the correct size. If it was, the section would have been 1/20 of the total area. The angles on the sections were too acute to be able to slot them together to make a point from 5 of them, like an icosahedron. This is another reason why 1/24 fits, since the sections are too small for 1/20, they must be less than 1/20 of the total volume.

 

[Kappa]

So its 4 spheres? as in Balls?

If I'm barking up the correct tree, then when they are at rest, like on a table, yet together, imagine a Cube, each vertical side of the cube runs at the centre point of each sphere, and the top and bottom of the cube is at the top and base of the spheres. Kind of linking them, If you get what I mean

Therefore, the VOLUME of space would be the Volume of the cube i.e. Sphere Diameter^3 less the volume of 1 sphere. As if you imagine the cube, there will be one quarter of each sphere within it.

BOOM! (i hope!)