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### Finding the Radius of a Pipe

```
Date: 1/28/96 at 1:30:40
From: Anonymous
Subject: Geometry

A pipe has become bent and is no longer round.  In order for me to
correct the problem, I must build a brace to go around the pipe
and true it up.  However, until I can determine the radius of the
pipe, a brace cannot be built.

How do you determine the radius of a circle when all you know is
the circumference ?
```

```
Date: 3/4/96 at 21:53:30
From: Doctor Jodi
Subject: Re: Geometry

Hi there!

If you had the radius and wanted to find the circumference, you'd
use the formula:

circumference = pi * 2 * radius

(you may have also seen this written as pi * Diameter, since the

Now, since you have the circumference and want the radius, we need
to get the radius alone on one side of the equal sign.  We can do
this by using INVERSE OPERATIONS.

If this makes sense, you can skip this next part
------------------------------------------------
Addition and subtraction are inverses; so are multiplication and
division.

For example,

3 * 5 = 15

If we multiply each side by 2, both sides will still be equal.

2 * (3 * 5) =  2 * 15

we see that

2 * (3 * 5) = 30

2 * (15) = 30

30 = 30
-------------------------------------------------------------
We can do the same thing with the formula above,

circumference = pi * 2 * radius

We want to solve for the radius--that is, we want the radius alone
on one side of the = sign.

so first, we divide through by 2

circumference /2 = pi * 2 * radius / 2

which also equals

circumference /2 = pi * radius

Next we divide through by pi:

which can be rewritten

circumference /(2 * pi) = radius

Pi is a really cool number that doesn't end; one rough
approximation is 3.14

Your calculator will have a closer approximation.

-Doctor Jodi,  The Math Forum

```
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Practical Geometry

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