09 Jun 08
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.
09 Jun 08
2 edits
Originally posted by ScheelI think the number of chocolates (modeling them as spheres as you suggest) should be given by the following:
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
Originally posted by ScheelIs the bowl a cylinder, hemisphere, or sphere?
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
1 edit
Originally posted by LemonJelloYes that is also my thought.
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
Originally posted by ScheelDo you mean American footballs or soccer balls?
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
Originally posted by clandarkfireIf it is euro 2008 it will be the type of football which is given that nasty "s" word in the USA!
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
Originally posted by deriver69No, 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.
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
Originally posted by AThousandYoungI 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.
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.
