A sphere that has a radius of 5 m could contain how many spheres that have a diameter of 5 cm?

Question

I found the volume of the larger circle and divided it by the volume of the smaller circle. Is that what I'm supposed to do?

Answer 1

Dividing the volumes will not work, since there is space between the small spheres that is not accounted for.  That method will only give an approximate result.  However, the bigger the difference between the small and large sphere's diameter, the better the approximation.  Here the ratio of diameters is 200:1, so your method should give a good approximation .  The answer would be 200^3.

Answer 2

This problem can only be solved precisely by numerical analysis or by experimentation. You can easily establish upper and lower bounds by proving that certain arrangements are possible or not possible, but making your upper and lower bounds closer makes the calculation more and more complex.  

Answer 3

That is assuming that all of the smaller spheres could be packed together perfectly into the larger sphere.  Unfortunately, that is not the case, and I'll be damned if I know how to solve this problem...but let me know if you figure it out.

Answer 4

Be careful, a circle has no volume, it has area.  A sphere, has volume.  Your calculation is only correct if dealing with circles.

Answer 5

well if you could fill it up completely it would contain 200 since the radius is half the diameter the diameter of the big sphere is 10 m and the diameter of the small sphere is 5 cm and a cm is 100 times smaller than a meter you have to do 10 divided by 0.05 which comes up as 200