Solve This Math Problem

[Coss]

I may be selling this to someone you know. At $1.00 a yard there is considerable money at stake.

That's your deal, so good luck on it.
I would take all the answers, add together, average them out, add 12, divide by 3.16, invert, minus 64, divide by 2.903, compare it to the moon cycle, wait 16.83 hours (not a minute more or you'll have to start over) multiply by 14.096, plus the geo location = Charge the price that you think is fair to both of you

 

[Johnny Acree]

Weigh it,remove 1 yard weight it, total weight div by 1 yard weight equals yards?

 

[Chaz]

Try this calculator

of Material
Entered Values Calculated Values
Outside Diameter of Rolled Material (in) Thickness of Material (in) Diameter of Center Hole (in) Length of Material (ft)
= 1679.87941 ft long

 

[floydv]

I'll post a mathematical solution later.

 

[FC]

Would it be practical to count how many layers thick it is? Seems to be the only way to get a truly
accurate thickness of the material. The way I was doing it was calculating the area of the side of the roll,
Dividing that by the thickness to get the length. Then multiplying by the width to get area.
Problem being is that the thickness of the cloth has to be very accurate for that to work.

 

[ECAJohn]

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.

I included the decimal places to allow replicating the math, not to suggest that degree of accuracy. This is all approximate because the result is probably quite sensitive to how tightly the cloth is wrapped. If it is wrapped real tight, the cloth probably stretches and the thickness would be less. If wrapped loosely, then there will be void space that will inflate the apparent thickness of the cloth.

I would try to cross-check this result by looking up the weight per square yard for the cloth (if that is possible). You'd have to estimate the weight of the cardboard core and subtract that from the total roll weight, and then divide total cloth weight by the weight per square yard (that you looked up) to get another estimate of total square yards on the roll.

Here's some 0.012 inch fiberglass on Amazon that is labelled as 4 oz per square yard:

https://www.amazon.com/Fiberglass-Glass-Reinforced-Winding-Molding/dp/B01IRDJM82

 

[floydv]

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.

I included the decimal places to allow replicating the math, not to suggest that degree of accuracy. This is all approximate because the result is probably quite sensitive to how tightly the cloth is wrapped. If it is wrapped real tight, the cloth probably stretches and the thickness would be less. If wrapped loosely, then there will be void space that will inflate the apparent thickness of the cloth.

I would try to cross-check this result by looking up the weight per square yard for the cloth (if that is possible). You'd have to estimate the weight of the cardboard core and subtract that from the total roll weight, and then divide total cloth weight by the weight per square yard (that you looked up) to get another estimate of total square yards on the roll.

Here's some 0.012 inch fiberglass on Amazon that is labelled as 4 oz per square yard:

https://www.amazon.com/Fiberglass-Glass-Reinforced-Winding-Molding/dp/B01IRDJM82

Ding Ding Ding Ding. I used the same exact approach but haven't had time to post my solution. ECAJohn is right that it depends on how tight the roll is, so this solution assumes tightly wound with no material stretching (pun intended).

You can use an exact mathematical solution, but it's more complicated and doesn't get you much more accuracy than this approximation method.

 

[Buckeyejake]

I would convert to weight. Weight a square yard of product. Weigh the total product less the core weight. Divide the square weight into the total weight.

Eliminate tightness of roll and other variables in your calculations.

 

[ECAJohn]

I would convert to weight. Weight a square yard of product. Weigh the total product less the core weight. Divide the square weight into the total weight.

Eliminate tightness of roll and other variables in your calculations.

This is the way I would do it, assuming you are willing to sacrifice some cloth to weigh it.

That said, it was a fun problem to solve the other way.

 

[Buckeyejake]

If you are worried about waste using the weight calculation just make the initial size smaller and adjust your math. There are a number of ways to solve the question.