Yes.
Here, I have the densities for two candies:
Tootsie Rolls: 1.18 g/mL
Starbursts: 1.28 g/mL
I called up Wrigley (the Starbursts company) and asked them for the average packing efficiency of their products. She asked me at first, “What do you mean?” Then I explained what it means to her and she said that they don’t know this information.
Well of course the front-line customer service person you get on the phone isn’t going to know that, any more than she would know, say, the chemical composition of the ink printed on the wrapper. You’re lucky if you get some who speaks Englyshe.
There must certainly be someone there who knows. That would be some marketing engineer who designs the packaging. It’s unlikely you can get to such a person by phone – you can’t get past that front-line customer service rep, who won’t even understand the question.
And you can’t get anywhere by e-mail. Your e-mail query will be answered with a vacuous generic form letter generated by their e-mail answering bot.
A written letter, delivered by the Postal Service, might have a chance. There’s more of a chance some live sentient human will see it, and somehow figure out who to pass it on to, IME. It’s possible the company will consider it “proprietary confidential data” however. But you can try.
Knowing the density does not really mean much if you don’t have the weight of the jar and sweets.
You can work this out yourself - buy a big bag of Starbursts. Choose a container with a known volume (say 1 litre). Fill with sweets - count. Repeat a couple of times to get a loose pack average. Then do it again, but shake and top up the container a few times to get a tight pack average.
Calculate the packing efficiency. This isn’t just math, it is statistics and scientific method, too. But don’t eat the sweets. That’s biochemistry, and the road to ruin 
Si
I don’t think we are done yet. Tomorrow (surprisingly) we’re doing a packing efficiency activity in mathematics. We have to bring in an object or two tomorrow. I’m bringing in a Jolly Rancher and a Starburst, just for the heck of it. Now, si blakely might have a point, but that’s just too much of a hassle. How can I buy so many of each candy. I mean I can, but my parents probably wouldn’t let me, and it sounds like an insane idea when we don’t even have a solidified answer for figuring out the volume of the jar.
The reason I say we’re not done with the volume of the jar, is we have to still figure out a procedure on how to figure out the volume of the jar using the cylinder concept, but with precision. I don’t want to be getting volumes off by more than 50 mL. We also still need to discuss the usual ratio of glass weight to candy weight (or mass rather), because that’s another tactic we have in the bag. If you trick the hosts into telling you the weight. Then if we know the amount of weight that is glass, then we can take that percentage out, and then divide the density of the candy from the mass to get the volume. Once you have the volume of the candy, you do not need to factor in packing efficiency because that mass was just the mass of the candies. I was wrong, there is no air mass in there. When you’re measuring the jar, there is not air mass inside. So as we all know (or should know), mass divided by density is volume. If we know the volume of all the candies combined, then all that’s left is dividing that by the volume of one candy and that’s the end of the discussion.
See, if we can fool them into telling us the weight of the jar, then we have that trick up our sleeves if we KNOW how much of that weight is actually glass. The problem is that to fool them, you’ll have to look innocent like you’re not trying to do anything. Start looking at it, and look like an average mathematically illiterate person who can’t even do algebra, “I think there’s 200 in there.” Then look very curious and ask for the mass of the jar. If it works that’s great. But only if we know the amount the glass is taking up from that weight. I know I said 20% is ideal for now, but that’s very rounded and estimated, and I’m hoping to find something more precise.
As for the cylinder method, we also need a way to do that precisely like I said. We can’t be getting results that are significantly inaccurate. Like I said, the tolerable threshold is 50 mL. But I would prefer to stay within 20 if possible. So if people have ideas to make these procedures as precise as possible, please share them, or at least discuss your ideas.
You think taking a photo could be a problem, but you think …
… is an acceptable approach :dubious:
And to point out the obvious - they don’t know the weight. I’ve run these sort of contests for fundraisers (I think I still have a big jar of lollie-pops left over from one), and I never, ever felt the need to weigh anything. Whereas people taking photos with cell phones is pretty common, especially if they are pointing it at a friend larking around the competition area.
Si
Because how are you going to get the diameter from a photo measurer. And even if you do, figuring out the volume is going to be a hassle, and too inaccurate if it’s irregular. At least with the cylinder method, it’s not complicated. All you have to do is pi(r)^2*h. And inaccuracies will tend to be small. And the mass method is also something that would be nice because you can get a better idea of what volume to aim for. There’s really no clear answer on this yet. And I would like to hear what Senegoid thinks about this.
Remember, you don’t need the absolute diameter of the gumballs or jar. You just need the relative diameters of the two, which you can get from a picture.
But how? How do you get that?
Use a ruler. Display the picture, for example that gumball machine, on your monitor. Maybe enlarge it to get better accuracy. Then measure how big a gumball is in millimeters, or inches or whatever is easiest. Measure how big the jar is using the same ruler.
You won’t get the real gumball diameter, but that doesn’t matter. You’ll get the same number of gumballs whether the gumballs are 1 cm in diameter and the globe is 9 cm, or the gumballs are 1 inch in diameter and the globe is 9 inches, or the gumballs are 1 foot and the globe is 9 feet.
Pick up a chemical engineering textbook, the idea of solid particle packing efficiency has been thoroughly studied. I know one of mine (Unit Operations of Chemical Engineering) has a bunch of formulas depending on particle shape, but I left it at work so I can’t help you tonight 
Hey Senegoid, long time no see.
Anyways, I just wanted to tell you that we have started a trigonometry unit with LOTS of cosines, sines, and tangents.
In my opinion, it’s very agitating. This is probably my least favorite type of math…always hearing cos, sin, tan…
Anyways, I just wanted to let you know since we did talk about when I’m going to be learning Trigonometry.
I’m curious about how your math classes and topics are organized. Is this part of your Geometry class? Back on my home planet, we had a full school year of Plane Geometry (with a week or two of solid geometry squozen in toward the end), then another (second) FULL school year of Algebra, then a full semester of Trig, then a semester of “Math Analysis” (what we called Pre-Calculus).
But when you write “started a trigonometry unit” it sounds like you’re just getting a few weeks wedged into your Geometry class? Say it ain’t so, Anonymous User! Why is it agitating? It’s just a fancy application of Algebra, really.
Have you learned any Analytic Geometry yet, even a little bit? Like the equations for all the conic sections and how to recognize them on sight and identify what the graph looks like, and how to complete squares to put equations into a conic-recognizable form? All you get are conics with vertical or horizontal axes.
Later (like, squozen into a week or two of 2nd- or 3rd-semester Calculus) you get to do conics with axes that aren’t vertical or horizontal. Then you get to see LOTS of sines and cosines. You have a set of sineful and cosineful equations to rotate such a conic to make it orthogonal to the axes. I discovered that you can put those equations into a nifty neat matrix form. Have you learned anything about matrices yet? Really nifty stuff. Y’oughtta look into that too.
Just wait until you get into solving trigonometric equations and memorizing page after page of useful trigonometric identities, and pages of problems where you prove additional identities just for practice! Counting candies in a jar will seem like child’s play after that! 