In this lesson you will learn how to find the
circumference of a circle.

"Pi "
Many, many years ago mathematicians discovered that no matter what size circle they worked with, the ratio of the distance all the way around the circle (the circumference) to the length of the diameter always was a little more than 3.14, or 22/7.
About 100 years ago they were able to determine that this ratio never came out to an exact number, in fact they have calculated this ratio out to over a million decimal places and it still never ends.  We call these types of numbers, "irrational numbers."
In any case the name they have given to this ratio is "pi" and they assigned the
Greek letter "Π " as it's symbol.
The way to represent this ratio symbolically is:
Π = Circumference/diameter
or
Π = C/d
 

The "Circumference" Formula:
Since no matter what circle we use, if you multiply the length of the diameter by this mysterious ratio we call "pi" we get the distance all the way around the circle, the formula for circumference is:

C = Π x d

Find the circumference of a circle having
a diameter of 14 inches.
(let Π = 3.14)
Simply take the formula for the circumference and plug in the given information.
C = Π x d
C = 3.14 x 14
C = 43.96 inches!

A circular flower bed has a radius of 17 feet.  How many feet of fencing (to the nearest foot) will we need to completely enclose the garden?
(let Π = 3.14)

Ok, now before we solve this one, we have to be careful not to make a mistake that many, many students make in a problem like this one.
Did you catch it??
That's right! The problem gives you the length of the radius, but the formula needs the diameter ! So, before we do anything else we need to change the radius into a diameter.  And since a radius is 1/2 the length of a diameter, all we need to do is double the radius and presto...it's now a diameter!
If r = 17 then;
d = 2(17) = 34!
Now plug into the formula:
C = Π x d
C = 3.14 x 34
C = 106.76 feet
To the nearest foot: C = 107feet
We need 107' of fencing.
 

This is a diagram of Pete's basketball court.  He wants to put a fancy tape stripe around the boundary of the court but he needs to know the distance so he can purchase enough of the special tape.
Using 3.14 for pi, find the distance around this shape.

Hopefully, you can see that this problem involves finding the perimeter of 3 sides of a rectangle and adding 1/2 of the circumference of a circle. The other important point to note is that the diameter of the circle is equal to the dimension of the rectangle directly across the shape.
Let's do it!
P = 14 + 25 +14
P = 53 feet
C = Π x d
C = 3.14 x 25
C = 78.5
78.5/2
(Remember, only 1/2 the circumference)
Distance around the semicircle is 39.25
Now add the 2 measures:
53 + 39.25 = 92.25 feet
Pete will need 92.25 feet of the tape.