|
"Circumference"
The circumference of a circle is the name we give for the
distance around a circle.
Unfortunately, because it is impossible to measure circular
distance as easily as it is to measure straight sided
distance, we need to introduce a very important mathematical
concept before we continue.
|
|
|
"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 |
Let's start with
an easy example.
|
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!
|
Got the idea?
Let's try another..
|
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.
|
Now let's look
at a tough one..
|
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.
|
|
