Solve This Math Problem

[Rob Croson]

Weight is how they would do it for inventory, if it was that critical to know the exact amount. (Usually that's not necessary for partial rolls.) If your scale is sensitive enough at both the low and high ends, you get very accurate results. That's how they inventory things like bulk screws, washers, etc.

 

[Rob Croson]

I came to an approximate solution to this by adding up the circumferences of concentric circles, starting at radius 2 inches, and increasing the radius by 0.015 inches between wraps. The circumference increases a little with each wrap as the roll grows. An Excel spreadsheet makes it easy--set up the code to do the math, and then copy down until the radius is 9 inches (approximately).

468 wraps gets the radius to 9.005 inches, and the cumulative length length is 16,180.27 inches (= 1,348.36 feet = 449.45 yards). The width of the roll is 38 inches = 1.055 yards, so the area (the product of length and width) is about 474.42 square yards.

This is exactly what I did, except that I calculated based on diameter. I think we got the exact same answer.

 

[NSTG8R]

Here's the formula for anyone that has some spare time on their hands.

t = material thickness
ro = outside dia. of the roll
rI = inside dia. of the roll [o.d. of the tube]

 

[ECAJohn]

This is exactly what I did, except that I calculated based on diameter. I think we got the exact same answer.

I see that Rob--I must have missed your post. The answers look the same (as the should). You win the prize!

Spreadsheets are great tools, don't you agree?

 

[Ty]

This is not correct. You are only accounting for one layer of cloth per wrap. When you wrap the cloth around the roll, you are adding a layer to both the left and the right sides. So the diameter goes up by 0.03" with every wrap.

LOL... no.

 

[Frim]

I wish!

well lets see how rusty my math is getting.



9(squared) x 3.14159 = 254.469 area of 18in circle

2(squared) x 3.14159 = 12.566 area of 4 in circle

254.469 - 12.566 = 241.903 area of cloth

241.903 / 0.015 = 16126.867 inches long area of cloth divided by thickness

16126.867 / 12 = 1343.906 feet long converting to feet


16126.867 * 38 = 612820.946 square inches area of cloth in sq inches


612820.946 / 1296 = 49248 square yards converting to square yards.

Would you like to buy some cloth? I have a bolt for sale. What color do you want?

 

[Frim]

Here's my super-fast estimate and how to do it...

Outside diameter = 18" 18* 3.14 = Circumferance... or 56.52 inches. or 1.57 yards... width is 38" or 1.05 yards.. That means the first wrap is 1.6485 square yards. Easy, right? Lets do the same for the inside-most wrap.. 4"X3.14=12.56" or 0.3489 yards X 1.05 yards =.366.

How many wraps are there? 18"-4"=14". Each wrap takes 0.015" so 14/0.015= 1000... The AVERAGE yards per wrap (max+min / 2) is 1.00725 square yards... So, 1,000 wraps times 1.00725 yards equals ROUGHLY 1,000 square yards.

Since that's a big, round number, I'd guess you have a 1000 yd ^2 roll there.

I will go with this one. Or, the answer is one bolt. Because cloth is sold by the bolt.

 

[Frim]

so a train is going east at 53 mph, and another (237 miles apart) is going west, on the same track, and at sunset, at 47 mph what time will they collide
Who gives a s_ _t, Just my 7th grade math teacher?

2.37 hours later. What does sunset have to do with start or finish?

 

[Ty]

Time for me to give my solution. ( It is fiberglass cloth which miked out at 0.012. Not tightly wrapped so I used 0.015--maybe should have been even higher.)

The thickness of the layers is 7". (18/2 - 4/2 = 7")
Calculate the number of layers in 7". (7/0.015 = 466.67 layers)
Average length of a layer--7"/2 gives the middle of the thickness and has a circumference of 34.557"
Number of layers x circumference gives length of cloth. (466.67 x 34.557" = 16,126.7")
Convert to feet. (16,126.7"/12 = 1343.9')
Convert to sq. yards. (1343.9' x 38/36 = 1418 sq. yards)

Anyone see a mistake in my calculations?

Thanks to all who worked out a solution.

The smallest layer would be the 4" diameter layer... THAT would be pi*D=Circumference... So, 3.14 * 4 = 12.56 inches. So, the average can't be 7" as you state.

You converted length to feet but should have converted it to yards. you didn't find sq. yards there. If you had further divided your 1343 by 3 to get to yards, you would have gotten square yards. It would have been easier to just divide your length in inches by 36 to get yards.


Largest circumference is pi * 18 = 56.52. The smallest is 12.56. The average is 34.5... Okay, yeah. you had it stated differently there but it's the same.

34.5 * 466.67 = 16100 inches or 447.23 yards. It's 38" wide or 1.056 yards wide... 447.23 * 1.056 = 472.27 square yards.

I must have made a mistake earlier but man, 1,000 square yards is a nice, round number.

 

[Ty]

I'd bet that at 400+ wrappings, most of the layers will be pretty tight and that you'll be closer to .012 than .015. So, figure that out in your calculations.