And yeah, I’ll take some razzing on this one, since I don’t remember the relevant math at this point in my life. 
I was making a big batch of meatballs, with a recipe that stated yield as approximately 80 1.5" meatballs. I decided to make them smaller (about 1"), and got closer to 220. I would have expected around 120, working from the ratio of diameters, but can’t remember calculating volume well enough to figure out how I got the result I did.
The volume of a sphere is: (4/3) * (pi) * (radius CUBED)
The cubed part is what throws of both you and everyone else in this kind of situation. It means that if you increase the radius by only 50%, the new volume will be 270% larger.
270% of 80 is 216. I’m amazed at how close you got!
PS: Increasing the diameter by 50% is exactly the same as increasing the radius by 50%. You probably knew that, but I just wanted to make it clear.
PPS: Ooops. My bad. 1.5 cubed is 3.375, not 2.7. Can’t do arithmetic today. You should’ve ended up with 270 meat balls.
So some were apparently oversized. Results were 2 pans of 80, 1 pan with 66. If I can add today :), that’s 226.
Thanks for the refresher on volumes. That does explain the rather surprising yield.
you won’t get razed, meatballs are no laughing matter.
270 balls would be it.
The diameter was decreased.
The change in the number of meatballs is a factor of (.75/.5)^3 = 1.5^3 = 3.37.
80x3.37 = 270. I suspect the meatballs were a bit larger than 1" if you only got about 220.
By about 1", I presume you mean roughly 1.0609" in diameter, at a guess?.
:). Not the most precise measurement, I admit (I was using a melon baller as a scoop), and I did see some minor size variance in the finished product. If the diameter you give would have gotten me the yield I did, then you’re probably right.
The fact that volumes scale as the cube of the diameter (or radius) gets quite interesting when you start looking at astronomical objects. For example, the diameter of the sun is about 110 times the diameter of the earth, which doesn’t seem all that much, until you consider that the volume of the sun is 110 ^ 3 = 1.3 million times the volume of the earth. In other words, pretty damn huge.
This is why giant animals in monster movies are unrealistic. If you take an animal (like an elephant, say) and enlarge it to twice the size (i.e. it’s twice as tall), it has eight times the volume (and is presumably eight times as heavy), which its legs, which have twice the length and four times the cross-sectional area as before, would be unable to support.
You counted to 220? Wow. After 25 or so I would’ve eyeballed it. Unless I had 220 extraordinarily important people coming over.
One of the few exact illustrations I remember from Tufte’s seminal The Graphical Display of Quantitative Information is one that he abhorred. You still see variations of it.
It was a timeline or something to show how the price of gas went up. At each date an illustration of a barrel was shown, in false 3-D. Well, when the price went by half, the same illustration was shown 1.5 times larger; by 100%, twice as large. All very pretty and understandable, I guess, but absurdly incorrect. Indeed, correct illustrations of the cube multiplication of volume would have been all the more informative (and dramatic, if you want to look at it that way).
Went on the number I got on each pan load. 
(2 pans of 80, 1 pan of 66)
Dude, now you’ve totally ruined The Attack of the 50 Foot Woman for me!
I believe with metabolic effects it would also burst into flames.
So a dragon is an iguana who escaped the FX set of a monster movie?
Now, who will help you eat the meatballs?
I will! I will! I will!