## Monday, April 26, 2010

### WCYDWT: Oranges

Oranges are packed and sold using a standard box...

and contain fruit that is all the same size (kinda) based on average diameter...

which is determined using this:

They come in 10 sizes: 36, 40, 48, 56, 72, 88, 113, 138, 163 and 180 which is based on the number of pieces of fruit that can be packed in the box.

#### 6 comments:

CalcDave said...

Could lead to great things: http://en.wikipedia.org/wiki/Packing_problem

David Cox said...

It could, but how would you present this to your class?

Anonymous said...

I immediately see questions of packing efficiency in the pictures provided. How can I get the most fruit into that box?, being the most obvious.

Put me in a geometry class and I'm experimenting with volumes of spheres inside rectangular prisms.

I wonder aloud in front of my kids if there's a better standard orange box size.

Ian Byrd said...

You could determine the wasted space by finding the volume of the cube that surrounds the sphere and then subtracting the volume of the sphere. Multiply by the number of oranges packed in there to find the total empty space in the box. Perhaps figure out the cost of that wasted space UPS or FedEx information?

CalcDave said...

Ian, that only works if you're packing spheres as you would cubes, which is not always best. Once you have the first layer down, you don't want to balance the 2nd layer directly on top, you want them to sit in the pits between the oranges on the first layer.

I might present it to the class with pictures first as you've done here. Maybe ask them to guess or work through a basic estimation of what size a "36" orange would be. (start with 2D circles and then ask how a 3D model might change things) Then bring out a crate of 36 oranges.

See if their guesses were right and also ask them to pack the 36 oranges into the box. What's the best way to fit them in?

Maybe then do some of the smaller sizes. Then ask if there were a more efficient way if you could mix the sizes. Have a bunch of different kinds and see who can play with it to get the most oranges in the box without squashing them or breaking the box.

Now, can we design a better box? Who (in real life) cares about this stuff besides orange farmers? Where else is packing important (I grew up in Memphis, so we'd immediately think of FedEx, but your kids may think of backpackers). If nobody suggests it (and I don't know why they would) you could talk about lattices in crystals and chemistry.

Ian Byrd said...

Ack, thank you Calculus Dave. Perfectly balanced, perfectly spherical oranges is a bit unlikely, I guess :)