Length of a Roll of Carpet
Date: 08/21/97 at 15:41:38 From: Shane Massey Subject: Length of a roll How would one determine the length of a roll of (say carpet) without uncoiling it? You are allowed to measure the thickness of the carpet and the diameter of the roll. I started by letting the thickness of a layer = delta x, but I did not make much headway.
Date: 08/22/97 at 11:16:10 From: Doctor Guy Subject: Re: Length of a roll Let's say you have a roll of carpet that has an outer radius of exactly 12 cm and an inner radius of exactly 4 cm (sort of like a roll of paper towels, in that there is an empty space in the middle) and the carpet is exactly 1 cm thick. The way I would calculate the length of the carpet is this: find the area of the region between these two circles (the "washer") and then divide this by the thickness of the carpet. The area of the region is pi*12^2 sq.cm - pi*4*4 sq.cm = pi*(144-16) = 128*pi or about 401.92 sq.cm. Now if you divide this by the thickness of the carpet, you would get a length of about 402 cm (rounding off), or 4 meters (about 12 feet and some). The units work here, which is not only nice, but essential. For more information on how to solve these kinds of problems, as well as alternative methods for solving them, have a look at these problems from our archives: http://mathforum.org/dr.math/problems/dorsey7.31.html http://mathforum.org/dr.math/problems/d14now.6.21.96.html http://mathforum.org/dr.math/problems/filip24.html -Doctor Guy, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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