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 
Diameter is twice the radius).

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:

(circumference / 2)/pi = radius

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