Quick geometry question, I want to fill a box with dice!

Uriel

So it's been a while since I did this math, and I'm trying to figure out a rough estimate of how many 16mm² six sided dice will go into a particular box.

The box in question is a army surplus 7.62 m82 blank 200 cartridge box (I've had it for forever for this intended purpose and just never got around to getting bulk dice but they are cheap enough on amazon now) The measurements of the outside of the box (until I get my tape out and actually get in it to measure around the gasket and such for more accuracy) are 7x3.5x10 inches

I just don't remember well how to use the formulas for area and volume to figure this out! I figure it'll be pretty fast with a little help though.

MrTLicious

Realistically you're not going to be putting the dice in at weird angles to maximize the number of dice you can fit in the box.

So, you just need to figure out how many dice fit in each dimension: So for example, take the length of 7 inches (177.8 mm) and divide that by the length of a die:
16mm, to get 177.8/16 = 11.11... So you can fit 11 dice in lengthwise.

Similarly, you can fit 5 (88.9/16 = 5.55...) dice in the 2nd dimension and
15 (254/16 = 15.875...) in the 3rd dimension.

So you'll have a 11x5x15 cuboid of dice, which fits 11x5x15 = 825 dice

Xaquin

area is Length x Width

volume is Length x Width x Height

so the exterior volume of your ammo box would be 245 cubic inches

Heffling

So 16mm is 0.23622". This means that you will be able to fit:

Along the 7" height, 7 / 0.23622 = 29.63 dice. As you won't be slicing up your dice to fit, this means 29 dice.
Along the 10" length, you can fit 42 dice.
Along the 3.5" width, you can fit 15 dice.

The total number of dice you can fit is then 29 x 42 x 15 = 18,270.

MrTLicious

FYI I did a calculation wrong on the first go round that I've edited. It's fewer dice than originally posted.

Uriel

Thanks!

And yeah it's a lot. but if you've ever played wargames and were as prone to losing d6s as I am you might understand my desire to fill such a large box.

Honestly with the gasket it's probably going to be a lot less too (can't use the full 7 inch / 177.8mm height I imagine it's closer to 4 or 5 inches), I'm also planning on painting the outside to be more thematically appropriate for games.

another option I have since I'll be painting the box anyway is to finish the inside with extra material like padding and felt. that'll make the internal volume much more manageable to fill plus more level so the dice will settle in even layers instead of at odd angles.

Daenris

Heffling wrote: »

So 16mm is 0.23622". This means that you will be able to fit:

Along the 7" height, 7 / 0.23622 = 29.63 dice. As you won't be slicing up your dice to fit, this means 29 dice.
Along the 10" length, you can fit 42 dice.
Along the 3.5" width, you can fit 15 dice.

The total number of dice you can fit is then 29 x 42 x 15 = 18,270.

FYI it looks like you converted 6mm to inches, not 16mm. 16mm is approximately 0.629921 inches.

Mugsley

25.4 mm per inch!

@Uriel you may be able to find internal dimensions on Ebay or Amazon for similar listings. Then reduce ~0.5mm in each dimension for your planned liner.

I may be saying something obvious, but do you have a dice tower for all that rolling?