Associated Topics || Dr. Math Home || Search Dr. Math

### 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
```

```
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/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Practical Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search