1. The circumference and Area of a circle

2. What is the formula relating the circumference to the diameter?
centre
Diameter
Radius

3. This means APPROXIMATELY EQUAL TO
C = ? x d
People knew that the circumference is about 3 times the diameter but they wanted to find out exactly.
C ≈ 3 x d
This means APPROXIMATELY EQUAL TO

4. Investigating the relationship between the circumference of a circle and its diameter?
Click on the link below and read the instructions.
Use the applet to create circles with different diameters.
Roll the circles on the number line to measure the circumference.
Your goal is to discover the mystery number in the formulae by
dividing the circumference by the diameter for each circle.
If you measure and divide corectly you should always get the same value for the ratio circumference/diameter

5. The mystery ratio 3.14 is very good and close to the true value
What value did you find for the ratio?
is pretty good
3.14 is very good and close to the true value
For most circumstances we say
Circumference ≈ 3.14 x diameter
What is the true value of this mystery ratio?????

6. Archimedes, said C ≈3.1419 x d Early Attempts
Egyptian Scribe Ahmes. in 1650 B.C. said C≈ x d
Archimedes, said C ≈ x d
Fibonacci. In 1220 A.D. said C≈3.1418xd
What is the value of the number that multiplies the diameter to give the circumference????

7. The exact true value is……………
UNKNOWN!!

8. An approximation to π
π≈ forever….

9. Videos on Circles http://www.youtube.com/watch?v=eiHWHT_8WrE
A Rap about circles
Circle Song2

10. What about the AREA of a circle?
First consider a square
The area of this square
in terms of r is
A= 2r x2r = 4r2 r 2r

11. What about the AREA of a circle?
Now consider a circle inside the square
The area of the circle must be less than the area of the square
A < 4r2 2r r 2r
Area = ? xr2

12. Finding a formulae for the area of a circle

13. C= πd or C=2πr
Semi-circle=πr πr r

14. Area of Rectangle= Base x Height
Area = πr x r
Area =πr2

15. The Area and Perimeter of a Circle
A circle is defined by its diameter or radius
radius
The perimeter or circumference of a circle is the distance around the outside
The area of a circle is the space inside it
Diameter
The ratio of π (pi)
π is an irrational number whose value to 15 decimal places is
π = We usually say π≈3.14
The circumference is found using the formula
C=π d or C= 2πr (since d=2r)
The area is found using the formula
A=πr2

16. The Area and Perimeter of a Circle
A circle is defined by its diameter or radius
radius
The perimeter or circumference of a circle is the distance around the outside
The area of a circle is the space inside it
Diameter
The ratio of π (pi)
π is an irrational number whose value to 15 decimal places is
π = We usually say π≈3.14
The circumference is found using the formula
C=π d or C= 2πr (since d=2r)
The area is found using the formula
C=πr2