Solve this

Dylan W.

Dylan W.

lone resident of Bro-Lite Island
Joined
Mar 17, 2007
Location
Mocksville NC
Ok...I don't wanna unroll this. Its heavy and I'll never get it to roll back up properly.

So..who can run the math and figure out the linear footage of this roll of rubber flooring.

3/8 thick
13" total outside edge to outside edge
Cardboard cone is 3 3/4 "
20180428_151542.jpg


Don' forget to show your work! I need to learn this equation.
 
Circumference = pi x diameter

Outer layer = 3.14 x 13

Next layer = 3.14 x (13-6/8)

Layer 3 = 3.14 x (13-6/8 - 6/8)

Etc, etc, etc.

Then add them together.

I try not to think too hard on a day off, so I didn’t calculate it all out.
 
I got this.

You're doing the calculation, but I've derived the formula. Because the material is thick, I used the midpoint of each material layer for the diameter of the layer, for slightly better accuracy in bending. Still ignores the fact that it's a spiral and not just a bunch of concentric layers.
Count the number of layers for n, and do math.

math.jpg


Mic drop. I'm leaving to go night fishing, bitches.
 
Fabrik8 said:
I got this.

You're doing the calculation, but I've derived the formula. Because the material is thick, I used the midpoint of each material layer for the diameter of the layer, for slightly better accuracy in bending. Still ignores the fact that it's a spiral and not just a bunch of concentric layers.
Count the number of layers for n, and do math.

View attachment 267251

Mic drop. I'm leaving to go night fishing, bitches.
Click to expand...
That reminds me of the Diff Eq class I took...
 
I know there's already been a couple of correct responses to this...one of them cheating, but it's still a win. Let's see how a scientist would approach the problem...

This can obviously be approximated very closely to a spiral. After all, past the first couple wraps, it is a spiral. Attached is a derivation of a formula for arc length, since you specified to show work...

The first formula is a general formula for a spiral, where you begin with a constant (tube diameter) with a factor that increases the radius incrementally with a change in angle rotating about the origin -

r=a+b(theta).

IMG_1909.jpg


The integral above for arc length comes from the integral for the length of a line.

IMG_1910.jpg


Take that oompa loompa crap back to the Chocolate Factory playground. :eek:

tenor.gif

7cadbb3a187175df84daf794bd6d182199db24c0a43b85b90caae6986ae77ab2.jpg
 
I mean the online calculator and scooter have a delta of around 5%.

I want Dylan to roll it out now and see who is more accurate
 
Ron said:
I mean the online calculator and scooter have a delta of around 5%.

I want Dylan to roll it out now and see who is more accurate
Click to expand...

XJsavage said:
Roll it!
Roll it!
Roll it!
Click to expand...

I'm curious too..I was hesitant to post since the delta was that high...roll that chit out! :D
 
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