Circumference of a Straight Line Question

Factual Questions
1

Sorry for the ambiguous thread title. I wasn’t sure how else to phrase my question is such a short space.

Okay, this is involving garbage bags, and what diameter garbage can they’ll fit over. So, for instance, we have a garbage can with a 19 inch diameter, that’s a 59.7 inch circumference. Now we’re not sure what garbage bags to buy for it. They come in a variety of sizes, from 24 to over 30 inches, across the top, flat.
So, given that data, how do we know what garbage bags will fit our garbage can?

Already we’ve figured that it’s not the standard straight across dimension of the bag times pi. So, in the shop we have garbage bags that are 25 inches lying flat. That times pi give us 78.5 inches, which should fit over out 59.7 inch circumference garbage can, but it doesn’t.

Obviously the bag is losing size as soon as it’s opened up. I’ve tried breaking down the garbage bag dimension by half, but that still doesn’t work. For our 25 inch bag, that’s 12.5, which by looking at a opened bag, the diameter is much greater than that.

So, essentially, using the garbage bag example and given just the size of the opening lying flat, how can we determine what circumference garbage can the bag will fit over? Or conversly, given the size of the garage can, what size bag will fit over it?

My apologies in advance for any terms used inappropriately. I hope I’ve clearly conveyed what my question is. Oh, and the bags don’t give a capacity, and the sticker on the garbage can with capacity is missing. Either way, I’d like to find out how to determine if the bag will fit with the data given above. It’s kinda annoying that I couldn’t figure it out. Thanks for your time.

2

IANA Mathemetician, but it seems to me that if you take the “width” of the garbage bag and double it, that will give you the circumfrence when the bag is reshaped into a circle. Therefore, a bag that is 25" wide will have 50" circumfrence when you try to fit it into a round garbage can.

3

If you lay the bag flat, the distance across the top is 1/2 the circumference. So for a can with about a 60 inch circumference you will need a bag that measures at least 30 inches across when laid flat.

4

Yeah, your right. I figured it out. We did a test with the 25 inch bag, and tried to get a circumference from it. It’s about 2/3 of the width. But just messing with the calculator, I figured that since we’re dealing with circles it would make much more sense that the “about 2/3” would actually be pi. So, take the width, divide by pi, times that by two, times that by pi and you get the circumference of double the original width. Which seems so simple now. I’ll claim a brain fart as my excuse.

I think I approached this problem from the wrong side and came up with the answer in a round about way rather then with straight forward thinking.

Thanks for the reply, good to know that the round about way I came up with it works.

5

DANG - beat me to it! :wink:

6

Circumference = 2pr. (I’m using “p” for pi because I can’t figure out how to make the character.) 2pr = 2d (because diameter = radius x 2).

Using b to represent the bag’s width and d to represent the can’s diamter, the formula would boil down to: d = 1/2 p b, or “d = 1.57b”; the bag’s width needs to be slightly more than one and a half times the diameter of the can.

To figure it out without using pi, or for a non-round can, pick two opposite points on the can and measure around from one to the other.

7

Try to think of it like this. Your garbage bag that is 25" wide when stretched out has a total outside dimension of 50" (25" on one side and 25" on the other side). Whether you reshape the bag into a circle, square, triangle or any other shape, the total outside dimension (or circumference) will always be 50 inches.

8

Or, as an even better example, visualize a string 50 inches long. Now join the ends together. Assuming a 100% efficient join, no matter how we shape the string (circle, square, rectangle, triangle, octagon, or a sillhouette of Jay Leno) we still have 50 inches worth of string around the outside of our shape.

9

“Do NOTHING simply if a way can be found to make it complex and wonderful.”

10

Okay, that works. You must have read my mind. After getting two replies with simple, straight forward (and correct) answers I was puzzled that two people could come in a intuitively know the answer when I had to just through hoops to get the answer. That explanation makes sense on a simpler level. I pretty much took the way spingears quoted.

11

Different shapes have different perimeters. The perimeter of the circle is called the circumference, and it’s pi times the width. The perimeter of a square is four times the width. The perimeter of your flattened garbage bags is twice the width. Each shape has a different formula. But you all knew that.