What is the difference between these two Pi formulas?

Date: 01/30/2001 at 16:32:44
From: Cassie C
Subject: What is the difference between these two Pi formulas?

To find the circumference of a circle, I know how to use

1) Pi *Diameter
2) 2*Pi*R

But some people have told me about Pi*R*squared. What is that? and 
what is the difference between that and 2 * Pi R?

Date: 01/30/2001 at 16:42:44
From: Doctor Rick
Subject: Re: What is the difference between these two Pi formulas?

Hi, Cassie, thanks for writing to Ask Dr. Math!

Your expressions (1) and (2) are equivalent because the diameter 
equals twice the radius, so Pi * Diameter = Pi * (2*Radius) = 2*Pi*
Radius. Both expressions equal the circumference of a circle, as you 
stated.

The other expression is the AREA of the circle:

             2
  Area = Pi*R

If you attach units to the radius, you can see that one is a length 
and the other is an area. Suppose the radius is 3 inches. Then

  Circumference = 2*Pi*R
                = 2*3.14*3 inches (approximately)
                = 18.84 inches

  Area = Pi*R^2
       = 3.14*(3 inches)*(3 inches)  (approximately)
       = 28.26 SQUARE inches

The area of this circle is pi times the area of a square with sides of 
3 inches. Any circle has an area equal to pi times the area of a 
square whose sides are as long as the radius of the circle. That's 
what the formula says.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/