Just wondering.
So that people can wind coils for crystal sets on them, of course.
More like why does Quaker do it, with their more traditional hot cereal products? They package their grits and corn meal that way, too. Turns out they started the round box in 1915:
Quite possibly, they just wanted to be distinctive. Early on, the company seems to have been very aware of the value of packaging and promotions. Their more modern variations on oatmeal products aren’t packaged that way, and many of their competitors aren’t.
Not all oatmeal comes in cylinders, and not all other grain cereals come in boxes. But in both cases most brands come in boxes, because they’re more efficient to pack. (If you pack a bunch of cylinders into a carton, you end up with lots of wasted space, and therefore higher shipping costs.) If a company decides to use cylinders to package their cereal, oatmeal or otherwise, it’s almost certainly to effect a distinctive look for their brand.
Likely only because it has always been that way and now is a marketing tool. I would be very surprised to learn of any real reason.
Originally weren’t oats and grains sold from a barrel? Barrel’s are easier to move by hand because they roll. It did make shipping easier before machinery was available.
I always thought Quakers packaging mimicked the old barrel. Today it’s just distinctive packaging.
They are used differently, or at least I use them differently. You pour cereal (and then the milk) from the box to a visual idea of the quantity you want. I transfer my oatmeal, from a store-bought drum, plastic bag or box, into a round glass cylinder. I measure it out of there, and measure the water, before I cook it in a microwave, because I know it will expand over it’s 10 min of cooking time. Visually, they are much different in size after cooking. That’s one idea, anyway.
No speculation to add, but just wanted to point out that McCann’s Steel Cut Irish Oatmeal comes in an tin (?) cylinder. However, the rest of their products come in a traditional chipboard box. I think the packaging makes it stand out on the shelf and increases the consumer’s perception of quality. It must be good if it deserves a tin cylinder, right?
That’s what I tell my cat about his food, but half the time he still refuses to eat it. 
- Nitpick alert -
They’re rolled oats. Oatmeal is what you have after they’re cooked.
- Nitpick alert over. Resume speed. -
Why does Prince Albert come in a can?
(Just realized this sounds like a dirty joke, but it’s not.)
Every dictionary I’ve consulted, including the OED, gives both definitions.
After I posted, I thought of cornmeal, the dry stuff you buy in the store. I guess it’s a regional thing. I am corrected.
OTOH, a cylinder contains a larger volume for its perimeter than a rectangular container.
Making oatmeal this morning, and remembered that little girls used to make doll cradles from the Quaker box, er, cylinder. I don’t remember being able to use the standard cereal box for anything.
I worked for Quaker Oats for almost 4 years (and, specifically, on Quaker Oatmeal for over 2 years). Surprisingly, I never learned exactly why they started putting the oats in a round tube, though I would not be surprised if it was to have a distinctive package. As yabob notes, the company was a pioneer in a lot of marketing practices, and the round tube may well have come out of that.
Parenthetically, the Quaker Man’s name is Larry. Seriously. At least, that’s how he’s always informally referred to by employees. 
I’m going with this. It’s not easy to measure a specific amount of corn flakes directly from the box, but you generally don’t need to. On the other hand, oat meal is easier to measure from the cylinder. Is that consistent with other cereals that need to be measured?
Oats come in rectangular box fashion in the UK
In Akron he’s called Ferdinand, even though he’s not really supposed to represent Ferdinand Schumacher.
This is because rolled oats don’t flow or pour well. Cream o’ wheat flows, so you can pour it out of a box into a measuring cup through a small opening without too much worry of excess, so you don’t need to be able to return the excess back to the box. Most dry cereals like corn flakes also don’t flow very well, but it is not usually critical to measure them with accuracy.
To get oatmeal to come out the desired consistency (if you are the sort of person that is particular in that regard) you need to measure out the rolled oats and the water. A round open topped container makes it easier to dip a measuring cup into, and then strike off the excess back into the container. Pretty much the same reason for storing flour and sugar in canisters. By putting the oats into a functional canister-like package, you get to keep your branding message on the consumer’s shelf until the box is empty, which wouldn’t happen if she needed to transfer your product into a glass or metal canister prior to the first use.
Why round? Because you want the lid to come all the way off so you don’t have flaps getting in the way while you are using one hand to hold the measuring cup and the other to strike it level. By going round, you can make a paper lid that stays closed tight enough to keep most insects out…of course now oatmeal boxes have a metal rim and a plastic snap-on lid, but the tradition was established with a paper lid that telescoped over the box. Of course you could do that with a rectangular box, but that causes structural problems. The corners of a square paper lid would be weak points, the top of the open box won’t support itself well, so it will gap along the length of the sides unless you use much heavier paper. Think about those floppy gift boxes they use when you get a shirt for Christmas.
ETA a hijack: Now what I have always wondered about is how many layers of a Quaker holding a box of oats with a picture of a Quaker holding a box of oats with a picture of a Quaker… could you progress before the box became smaller than a molecule of the ink used to print the picture?
You can make pretty decent magazine files out of the standard cereal box, if it’s the right size. Just cut the box so it has this shape, and cover the box with contact paper or printed paper or fabric.
I never made a cradle from the oats cylinder, but then I didn’t play with dolls if I could possibly avoid it. I did enjoy using the cylinder as a container for other things, once it was empty. And I’ve seen some nice tote bags made with the cylinders as the base, covered with fabric and using a drawstring as both closure and handle.
Back to the topic, I eat both Cream of (whatever) cereals and oats. I think that both types of products have pretty practical packaging for the typical use.