I Can Use ? to Find the Circumference of a Circle

1
I Can Use ? to Find the Circumference of a Circle
Circles and the Number Pi
2
Parts of a circle
In circle O, OB is a radius AC is a diameter
3
Parts of a circle
The distance around circle O is called the
circumference of the circle. It is similar to
the perimeter of a polygon.
4
Break Into Small Groups

• Each group should have
• Three or more circular objects
• A spool of string
• A ruler
• Scissors
• Paper and pencil

5
Make a Table!
Object Diameter Circumference
Object 1
Object 2
Object 3
6
Measure Object 1

• Measure the diameter with your ruler and record
  it.
• Wrap string around the circle and cut the string,
  so that the length of the string is equal to the
  circumference.
• Measure the cut string and record it as
  circumference.

7
Measure Object 2

• Measure the diameter with your ruler and record
  it.
• Wrap string around the circle and cut the string,
  so that the length of the string is equal to the
  circumference.
• Measure the cut string and record it as
  circumference.

8
Do the same thing for the rest of your objects!
9
What is the C ? D?

• Who wants to share the circumference and diameter
  of one of their objects?
• Lets find the quotient
• Circumference ? Diameter ??
• Before we calculate do you think we will get
  different results with the different objects?

10
A Piece of ??

• The quotients are all approximately the same.
• If measured COMPLETELY accurately, this quotient
  is close to 3.14.
• It is not equal to 3.14, however. It has an
  infinite decimal expansion with no repeating
  patterns!!
• We call this number ?.

11
What is ??

• Because this number has no repeating patterns as
  a decimal, it is irrational.

?
3
.
1
4
1
5
9
2
6
5
3
5

12
More ?

• How many decimal places do you want to go to??
• Dont ask for more than 1 million, please!
• If you picked a digit 0 through 9 at random from
  the decimal for ?, every digit would have an
  equal probability!

13
How to Calculate the Circumference

• To calculate the circumference of a circle, the
  formula is C ? ? d
• Approximate the circumference of a circle with a
  diameter of 2 cm.
• Approximate the circumference of a circle with a
  diameter of 5 feet.

14
THE END