How many Smarties will fit in a coffee mug?

[securespark]

I was idly wondering if you could calculate this scientifically, rather than buying tubes of sweets!!

Could you take the diameter and height of a smartie, take account of a certain amount of "wasted" space where they do not fit snugly together and calculate how many would fit within the confines of a standard 1/2 pint mug?

And would it make a great deal of difference whether they were just tipped in, or placed in carefully to try and save space?

I know this is decidedly a*al, but can anyone come up with an answer?

 

[2scoops0406]

How big is the mug?

 

[petewood]

Is it still full of coffee?

 

[Richardp]

been to a church fete recently?

 

[Nige F]

vol. of mug= Pi.RsquaredH.assuming it`s clyndrical

 

[2scoops0406]

vol. of mug= Pi.RsquaredH.assuming it`s clyndrical

Yep, R = ? H= ?

 

[petewood]

vol. of mug= Pi.RsquaredH.assuming it`s clyndrical

That's easy, now formulate the volume of a smartie!

 

[2scoops0406]

Easy, assume it's an ellipsoid, then measure it's length, width (assume the same as it circular) and height. Calc it's volume 4/3 pi R * length * width * height.

Assume that the mug is a cylinder, calc it's volume.

THEN you need to do the clever bit, you need to understand how the smarties can tessellate into the cylinders volume, do the calculus, take max and min numbers, and the answer, as always, will be somewhere in the middle of the two numbers.

Trouble is there are quite a few assumptions here.

 

[nstreet]

They are all the easy bits, its more difficult to work out wasted space as you don't know how the smartie will fit in its space and its relationship to the others.

Does it count if you melt them down first?

 

[petewood]

Easy, assume it's an ellipsoid, then measure it's length, width (assume the same as it circular) and height. Calc it's volume 4/3 pi R * length * width * height.
.

So what would the difference be if it was a prismatic elliptic-type object?

 

[2scoops0406]

Easy, assume it's an ellipsoid, then measure it's length, width (assume the same as it circular) and height. Calc it's volume 4/3 pi R * length * width * height.
.

So what would the difference be if it was a prismatic elliptic-type object?

42

 

[notb665]

How do you know they are all the same size? You are assuming too much, goddammit.

The different colours are different sizes.

 

[empip]

Bung 100 smarties into a measuring flask cover with water, take reading, pour off water to second flask, take reading.. first minus second = volume of smarties. divide by 100 for approx vol per smartie.
Stack number of smarties in mug maintaining a pattern until level across horizontal section of mug, constrain smarties, fill with water to just cover smarties... pour off water to measure, this is the volume of the spaces twixt the chocs, given the method of stacking.
Divide by number of smarties stacked .. rough estimate of volume surrounding each smartie.. add this to the approx vol per smartie.
Given the same stacking method, and the same fitment this must be a reasonably close estimate of the smartie vol plus slack space vol. due to stacking.
Seems reasonable, then most things do after half a bottle of red ..

 

[AdamW]

Spot the theorists and spot the experimentists

Write to Nestlé. Ask them for the dimensional tolerances on Smarties, along with the distribution covering those within tolerances and those outside (the odd one will always slip through). Whilst you are at it, find out what temperature they pass through the machine at (again, tolerances and distribution!). And if you can get the temperature/volume function too that would be great.

Then, do Eddie's bit with tesselation, take into account the tolerances on the smarties (very important) and you will find your max gets bigger and your min gets smaller.

 

[2scoops0406]

A bit similar to how many nails in a kilo eh?