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September 14th, 2014, 07:49 AM  #1 
Newbie Joined: Jan 2011 Posts: 18 Thanks: 0  size a sheet to fit a tube?
I'm not sure if this is elementary math or something more advanced so I apologize ahead of time if I put htis in the wrong place. I have a large pot that needs to be lined entirely with a teflon sheet. The pot is 10" diameter, and 12" tall. I need to know how to figure out what size square sheet I need to buy that will fit inside the pot to line the bottom and sides. 
September 14th, 2014, 12:22 PM  #2 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 
Yes, this question is more complicated than it first seems. You can't line the interior of a round pot with a square sheet without wrinkles, but then you have to account for the surface areas of the wrinkles. It becomes easier if you can cut the square sheet to your will (perhaps this is what you meant?). The surface area of the interior is $$145\pi \approx 455.531 \text{ in.}$$ So you should get a square sheet with side length at least $21.5 \text{ in.}$ 
September 14th, 2014, 01:14 PM  #3 
Newbie Joined: Jan 2011 Posts: 18 Thanks: 0 
Yes I can cut the sheet to my will and wrinkles don't matter for my purposes. So from your math I could buy a 24"x24" sheet and if I stick it in the pot evenly, the shortest side should still reach the top of the pot (or above it), then I could easily just trim all the excess. 
September 14th, 2014, 06:04 PM  #4 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 
Well, no. I meant if you could cut the sheet into any shapes, then it will work. For example, to cover the sides of the pot (a $12$ by $10\pi$ rectangle, essentially), you could cut two strips of $12$ by $5\pi$ ($12$ by $15.71$) rectangles. You can then use the remaining sheet to attempt to morph it into a perfect circle of diameter $10$ (though I don't know if this is perfectly possible in a finite amount of cuts). 
September 14th, 2014, 06:26 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra 
You will need a 10" diameter circle for the bottom. We can easily assume that you will need to use a 10" square section of sheet to make this. (100 sq.in.). You then need, as eddybob123 said, a $12 \times 10\pi$ strip for the sides. The easiest way to make this all fit in a sheet is if we use a 12" x 10" section to make the base (more wasteful, but it is then the same width as the strip. We then need to be able to make a $12 \times 10(1+\pi)$ strip in order to cover the whole pot. That's 12" x 41.4", which can easily be done from a 24" x 24" sheet. (with a section 12" x 6.6" left over  plus the offcuts from making the circular base. Last edited by v8archie; September 14th, 2014 at 06:31 PM. Reason: Upload template. 
September 14th, 2014, 09:31 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988 
Teflon is also known as Polytetrafluoroethylene... 

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fit, sheet, size, tube 
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