# Balls in a Bowl

Scheel
Posers and Puzzles 09 Jun '08 21:07
1. Scheel
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09 Jun '08 21:07
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 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.
2. 09 Jun '08 21:472 edits
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.
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 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).
3. 09 Jun '08 21:54
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.
Is the bowl a cylinder, hemisphere, or sphere?
4. Scheel
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09 Jun '08 22:15
Originally posted by golfer1
Is the bowl a cylinder, hemisphere, or sphere?
A bowl shaped as a cylinder with circumference C is filled .....
5. Scheel
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09 Jun '08 22:211 edit
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).
Yes that is also my thought.
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.
6. clandarkfire
Grammar Nazi
10 Jun '08 00:43
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.
Do you mean American footballs or soccer balls?
7. 10 Jun '08 05:29
Euro 2008...
8. 10 Jun '08 13:22
Originally posted by clandarkfire
Do you mean American footballs or soccer balls?
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.
9. 10 Jun '08 13:56
Originally posted by Scheel
Balls in a Bowl
[joke]Does that explain your high pitched voice and non-existing facial hair?[/joke]
10. Scheel
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10 Jun '08 22:32
Originally posted by FabianFnas
[joke]Does that explain your high pitched voice and non-existing facial hair?[/joke]
Since this is a great night for Sweden, I will let it pass ;-)
11. Scheel
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10 Jun '08 22:34
Originally posted by clandarkfire
Do you mean American footballs or soccer balls?
As other posters have pointed out :
If I meant Rugby balls I would have written "Rugby balls"
12. Scheel
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10 Jun '08 22:41
Thanks for the suggestions
13. AThousandYoung
12 Jun '08 03:16
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.
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.
14. 12 Jun '08 15:39
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.
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.

P.S. I dont mind rugby of both codes I just dont think they are football.
15. wolfgang59
Mr. Wolf
12 Jun '08 18:18
Us Brits codified the game (as we did several others) but it was played all other Europe. We (England) cannot claim to have invented it.

And all over the world it is known as FOOTBALL. (Check out the F in FIFA)

Check out
http://en.wikipedia.org/wiki/Football