So this is on the behalf of another friend for a school assignment. The assignment is: Find how many soccer balls fit inside a cylindrical building. Obviously, since a soccer ball is a sphere, the resulting question is the title.
Initially my friend was working with a crate method, namely turning the spheres into cubes whose length was equal the sphere's diameter, and finding out how many cubes fit (with some estimates, this is easy enough). However, having my own doubts about the correctness of the method; I did some research on my own and came across close packing. From what I've gathered from previous Stack Exchange questions etc. the maximum density the sphere's can occupy in the close packing method is around 74%. However, I have yet to really understand how they derive this number. My own knowledge is only equivalent to an advanced class high schooler, so that's probably why this goes over my head. Would anyone mind clarifying why the maximum density is 74%?
Edit: I had some great responses, thank you very much for them! A few problems though:
- They just gave the formula. Finding the formula itself is easy enough to do, the real problem is finding out where the numbers come from ($N \, \le \, \frac{\pi}{3 \sqrt{2}} \frac{V_c}{V_s} \quad \approx \quad 0.74048 \, \frac{V_c}{V_s}$ is the formula that has been found). In particular, the $\frac{\pi}{3 \sqrt{2}}$.
- The formulas dealt with rectangular prisms / other containers, not necessarily cylinders.
I did find the following previous Stackexchange articles but did not understand them: Problem of packing spheres of radius $\rho$ into a cylinder
Thanks again to everyone who has help me so far :)