How many Men size basketballs fit into a 25' by 25' room?
5 answers
depends on the size of the Men, doesn't it? If they're homunculi, there might be a lot more of them.
the circumference is 29.5 inches
The diameter of one ball is 29.5/pi = 9.4 in.
The room is thus 25 ft * 12in/ft / 9.4 in = 32 balls wide
If you use a square lattice for the circle centers, then you can fit 32*32 = 1024 balls in the room.
Using a hexagonal lattice, you can fit more balls. The density is about .9069, meaning that 300*300*.9069 = 81621 in^2 will be filled. The area of one circle is pi*9.4^2 = 69.4 in^2, so that will allow 81621/69.4 = 1176 balls
The room is thus 25 ft * 12in/ft / 9.4 in = 32 balls wide
If you use a square lattice for the circle centers, then you can fit 32*32 = 1024 balls in the room.
Using a hexagonal lattice, you can fit more balls. The density is about .9069, meaning that 300*300*.9069 = 81621 in^2 will be filled. The area of one circle is pi*9.4^2 = 69.4 in^2, so that will allow 81621/69.4 = 1176 balls
Hmmmm. What is the ceiling height? Or, just on the floor?
This is a very famous problem in Math, it started in written history with Kepler.
http://mathworld.wolfram.com/SpherePacking.html
This is a very famous problem in Math, it started in written history with Kepler.
http://mathworld.wolfram.com/SpherePacking.html
Just the floor and thanks Steve
5 answers