- 09 Jun '08 21:07A bowl shaped as a cylinder with circumference C is filled with small balls (football shaped chocolates). The small balls stand at a hight of h in the bowl.

A loose estimate is that the small balls have radius r.

What is the number of balls in the bowl ?

This is actually a Euro2008 related competition we have at work.

I have a guess based on the respective volumes, that I can share.

But maybe someone could come up with an alternative method ???

I can not empty the bowl and count, neighther is there any way I can put it on a scale to measure the weight.

What would you suggest ?

PS : No, I will not share the chocolates. - 09 Jun '08 21:47 / 2 edits

I think the number of chocolates (modeling them as spheres as you suggest) should be given by the following:*Originally posted by Scheel***A bowl shaped as a cylinder with circumference C is filled with small balls (football shaped chocolates). The small balls stand at a hight of h in the bowl.**

A loose estimate is that the small balls have radius r.

What is the number of balls in the bowl ?

This is actually a Euro2008 related competition we have at work.

I have a guess based on the respe ...[text shortened]... e to measure the weight.

What would you suggest ?

PS : No, I will not share the chocolates.

[(Pi*R^2)*h*(PE)]/[(4/3)(Pi*r^3)], where R is the radius of the cylindrical bowl and PE is the packing efficiency of the chocolate balls. The h and r are as you defined them.

You would have to make an educated guess as to the packing efficiency. For close packed spheres I think it would be around 0.74. Not sure what it would be for football shapes. Keep in mind that packing efficiency for ellipsoids is better than that for spheres (http://www.barransclass.com/phys1090/circus/Emily_Sorensen.html). - 09 Jun '08 21:54

Is the bowl a cylinder, hemisphere, or sphere?*Originally posted by Scheel***A bowl shaped as a cylinder with circumference C is filled with small balls (football shaped chocolates). The small balls stand at a hight of h in the bowl.**

A loose estimate is that the small balls have radius r.

What is the number of balls in the bowl ?

This is actually a Euro2008 related competition we have at work.

I have a guess based on the respe ...[text shortened]... e to measure the weight.

What would you suggest ?

PS : No, I will not share the chocolates. - 09 Jun '08 22:21 / 1 edit

Yes that is also my thought.*Originally posted by LemonJello***I think the number of chocolates (modeling them as spheres as you suggest) should be given by the following:**

[(Pi*R^2)*h*(PE)]/[(4/3)(Pi*r^3)], where R is the radius of the cylindrical bowl and PE is the packing efficiency of the chocolate balls. The h and r are as you defined them.

You would have to make an educated guess as to the packing effic ...[text shortened]... better than that for spheres (http://www.barransclass.com/phys1090/circus/Emily_Sorensen.html).

PE is very close to 0,74 (Kepler conjeture) for spheres in infinite 3D space.

The packing is however not optimal dense, any thoughts on a way to cross check ?

Edit : I like the M&M reference. But for further calculations I think we can assume that Chocolate footballs are spheres. - 10 Jun '08 00:43

Do you mean American footballs or soccer balls?*Originally posted by Scheel***A bowl shaped as a cylinder with circumference C is filled with small balls (football shaped chocolates). The small balls stand at a hight of h in the bowl.**

A loose estimate is that the small balls have radius r.

What is the number of balls in the bowl ?

This is actually a Euro2008 related competition we have at work.

I have a guess based on the respe ...[text shortened]... e to measure the weight.

What would you suggest ?

PS : No, I will not share the chocolates. - 10 Jun '08 13:22

If it is euro 2008 it will be the type of football which is given that nasty "s" word in the USA!*Originally posted by clandarkfire***Do you mean American footballs or soccer balls?**

I would just assume 30% of volume is wasted then maybe check to see if you can adjust this to knock out someone else close. - 12 Jun '08 03:16

No, it was given the "s" name in England. 'Soccer' is short for Association Football. Therefore soccer is a more precise name; soccer is a type of football, as is rugby.*Originally posted by deriver69***If it is euro 2008 it will be the type of football which is given that nasty "s" word in the USA!**

I would just assume 30% of volume is wasted then maybe check to see if you can adjust this to knock out someone else close. - 12 Jun '08 15:39

I am aware the origins are in england. Just because rugby types wanted to call their game football and invented the "s" word it doesnt make it right.*Originally posted by AThousandYoung***No, it was given the "s" name in England. 'Soccer' is short for Association Football. Therefore soccer is a more precise name; soccer is a type of football, as is rugby.**

P.S. I dont mind rugby of both codes I just dont think they are football.