# Grains of Rice in a Cubic Foot

How many grains of rice are there in a cubic foot of rice? I’m trying to figure out a good way to explain to a child the numeric concepts of a million, a billion, and a trillion. So I want to be able to say something along the lines of ‘if this shoe box were filled with rice, it would be a million. If the shower were filled with rice, it would be a billion. If that house over there were filled with rice, it would be a trillion’, etc. I realize, of course, that it depends on what type of rice we’re talking about, so let’s just say your every day long grain Uncle Ben’s stuff. I Googled this to no avail, so now I’m throwing myself upon the mercy and benevolence of the smartest people I know. Future Dopers of America are counting on this.

:smack:
Never mind—I think I found my answer. Half a cup of rice contains about 5472 grains of rice. Multiplying this by 32 to get the number of grains in a gallon and then multiplying by 7.48 to get the number in a cubic foot yields 1309778. So the volume of a million grains of rice is represented by a cube 10.97 inches on a side. A billion grains is represented by a cube 9.14 feet on a side, and a trillion would be represented by a cube 91.4 feet on a side (a little bigger than your typical house).

Here’s a good place to explore size and numbers using a common object:

Mega Penny Project

Ooh—excellent, thanks. Pennies are better than grains of rice because they are of a consistent size and the volume of a given number of them can be predicted with exact precision. I was particularly impressed by the representation of a quadrillion pennies. Assuming that a Federation Starship is about the same length as the Sears Tower’s height, then the relative sizes of the Sears Tower and the quadrillion pennies looks to be about the same as the relative sizes of a Federation Starship and a Borg Cube. So a quadrillion pennies will fill a Borg Cube!

Washoe
A small nitpick here. Although the volume of a penny can be determined with precision, their “packing” is another matter. From experiments I’ve done, a jar of pennies is actually 50% pennies and 50% air. (You’d think the penny percentage would be much higher wouldn’t you?) Yes, as you can see I spend my time wisely.

Also, here’s a nice link if you want to do conversions:
http://www.1728.com/convert.htm
Yeah, it is my website but it is all free.

I love so much the american measurement system…

Clairobscur
Oh absolutely !!!
A US Gallon contains 768 teaspoons.
A cubic foot contains 957.5 fluid ounces.

Who needs them thar furin’ metrical systems when the 'Merican system is much more convenienter.

Also try hunting down Douglas Hofstadter’s Metamagical Themas column (Scientific American, 1980’s) on “innumeracy”. It has good examples of this sort of thing.

His classic “twelver” (a trillion) is the number of cigarettes smoked in the USA in a year, although I imagine that’s gone down a bit since the 80’s.

How about putting one grain of rice on the first square of a chessboard, two on the next, then 4, i.e. doubling each time?

You pass 100 on the 8th square, 1000 on the 11th, 100,000 on the 18th and soon reach some seriously big numbers.

To fill the board, you need a total of 18,446,744,073,709,551,615 grains (roughly ).

Washoe -

There are two great childrens books on this subject. One of them uses increasing numbers of peas inside of a house, increasing by orders of magnitude until the whole town is buried in peas. I think its called “Big Numbers”

Another uses Blue Whales as a units of measurement to show how big the world and universe are. I think its called “Is a Blue Whale the biggest thing there is?”

Both books a very cool even for nerdy adults like me. My kids love them.

[Yakov Smirnoff] In America you eat rice. In Russia rice eats you! [/Yakov Smirnoff}

You should have seen it when bushels (2150.42 in[sup]3[/sup]) and pecks (2 gallons) were commonplace. And then there were rods (16.5 ft.), chains (66 ft.) and links (7.92 in.).

I want to come visit your house. At 91.4 ft. by 91.4 ft, then one floor would occupy 8,354 sq. ft. of area and at 91.4 feet high it would, based on a nominal 10 feet per floor, be nine floors high for a total area of 75,186 sq. ft.

Any room for me? :rolleyes:

Actually some cubic feet don’t have any grains of rice in them. You have to be careful with these generalizations, you know.

I think the most optimal penny-packing you can do would be super-tall cylinders jammed together, or optimally-packed hexagonal planes stacked up. The packing ratio is then really good, since you’re tessellating a 60-120 rhombus. You can do the math yourself; I reached an answer of

π/(2√3) = 0.906899682, or roughly 91% efficiency.

That might present an issue—some really smartass kid might ask ‘doesn’t it make a difference how they’re packed’?

What about perfect spheres? If they’re ‘shaken down,’ will they always arrange themselves the same way? I could change the analogy to BB’s or marbles.

Washoe
Well, I guess I was the one who brought up the “packing” issue in the first place so I guess I’ll answer that (although Jurph is more than welcome to join the discussion.)

Anyway Washoe, when you were determining the volume of a grain of rice
you found this fact:
Half a cup of rice contains about 5472 grains of rice.
This fact allows for the manner in which rice grains “pack” themselves.

This is unlike the penny which has a measurable, standard volume but you are not taking into account the air space between the pennies when they are packed into a given volume. To me the way to do this would be to fill up a known volume (a measuring cup) and see how many pennies it takes to fill that up. As I’ve said, I think the pennies will “naturally” occupy about 50% of the volume.

Perhaps you can save this experiment for the “smartass kid” you mentioned and have him do this research!!!

I remember a local elementary school trying to get a “million beans” together. We live in a fairly wealthy area, so buying a million beans was no problem, but the schools wanted to have the kids actually count the beans as they were added to the “Pile.” After loosing count twice, they decided to estimate by volume, after counting a representative scoop.

The picture in the paper showed a fair-sized kid’s wading pool, overflowing with navy bean sized beans of a number of different types. That was in the seventies.

I think barley grains would be a better choice. They are smaller, and after the big event, you could make beer.

Tris