Solve This Math Problem

[Sethodine]

>100 square yards

 

[CompTrex]

http://www.handymath.com/cgi-bin/rollen.cgi?submit=Entry

Entered Values Calculated Values
Outside Diameter of Rolled Material (in) Thickness of Material (in) Diameter of Center Hole (in) Length of Material (ft)
18 .012 4 1679.87941

5317 Sq ft.
590 Sq Yds.

 

[Ty]

18"-4"=14"
14"/.015=933 wraps...

Now, the tricky part.... The diameter changes with each wrap. I'm going to do it in excel but basically, I'm going to give you an answer in square inches...
Diameter * 3.14 = Circumference
18 * 3.14 = 56.52 inches * width of 38" = 2,147.76 inches square... or 1.657 yards... I'll save you the 933 iterations but the 2nd one looks like this:
(Previous diameter of 18" - 0.015) * 3.14 * 38" = 2,145.97" / 36/36= 1.656 yards... it continues... till it gets down to a diameter of 4" which gives you a grand total of 946 square yards of material.

 

[FC]

I should not do math late at night. I got the last calculation wrong it was 472.856 square yards.
The issue is that the question might be incorrect. Looking at wiki there is no regular cloth that is
0.015 in thick, maybe 0.15 think which would make it 47.2856 square yards.

 

[Ty]

It's funny that we all come up with different answers... or sad.

 

[Ty]

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.

 

[Johnny Acree]

Oh! I see! The answer is not wrong, the question is!

 

[Ty]

Easy answer is100yds because cloth is sold in easy numbers.

1,000

 

[Rob Croson]

Each wrap takes 0.015" so 14/0.015= 1000...

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.

 

[floydv]

This is technically a problem involving solving an equation for a spiral, but when the layers are this thin you can approximate it as a series of concentric circles/rings with a fixed thickness of 0.012" (or 0.015" as later suggested by the OP).