Take a hollow sphere, a basketball, for instance. Next, take smaller spheres: either softballs, ping pong balls and bbs, etc. The question is how much of the volume of the sphere is taken up by these other spheres if the basketball is filled to maximum capacity? Scenario A would fit as many softballs into the basketball, Scanario B would fit as many ping pong balls, etc.
Intuition seems to say that the smaller the spheres, the more of the volume that would be taken up. On the other hand, the sphere that would take up the volume most efficeiintly would be a single sphere that is just slightly smaller than a basketball.
I guess the questions are: is my intuition misleading me? Meaning that although it appears that the bbs take up more of the space, that they are taking up no more space than the few softballs that would fit inside the basketball
Also, what would an equation look like for this? And if plotted on a graph (amount of space taken up on one axis and diameter of spheres used to fill the basketball on the other, is the line straight ? Curved? Does it form a line then break when we use a sphere just slightly stronger than a basketball?
Feel free to offer an answer in a way other than what I described. Obviously, math is not my first language, so take it easy. Thanks.