circumference and area

8/2/2019 Circumference and Area

1/15

The circumference and Area

of a circle


2/15

Diameter

centre

What is the

formularelating the

circumfereneto the

diameter?


3/15

People knew that the circumference is about 3times the diameter but they wanted to find out

exactly.

C = ? x d

C

3 x dThis means APPROXIMATELY EQUAL TO


4/15

The mystery ratio

What value did you find for the ratio?

3.1-3.2 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 valueof thismystery ratio?????


5/15

Early Attempts

Egyptian Scribe Ahmes. in 1650 B.C. saidC3.16049 x d

Archimedes, said C 3.1419 x d

Fibonacci. In 1220 A.D. said C3.1418xd

What is the value of thenumber that multiplies the

diameter to give thecircumference????
http://personal.bgsu.edu/~carother/pi/Pi3a.htmlhttp://personal.bgsu.edu/~carother/pi/Pi3a.html


6/15

The exact true value is

UNKNOWN!!
http://en.wikipedia.org/wiki/Pi


7/15

An approximation to

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372

4587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609................forever.


8/15

Videos on Circles

http://www.youtube.com/watch?v=eiHWHT_8WrE

A Rap about circles

http://www.youtube.com/watch?v=fogehnFNDw0&feature=related

Circle Song2

http://www.youtube.com/watch?v=lWDha0wqbcI&feature=related
http://www.youtube.com/watch?v=eiHWHT_8WrEhttp://www.youtube.com/watch?v=eiHWHT_8WrEhttp://www.youtube.com/watch?v=fogehnFNDw0&feature=relatedhttp://www.youtube.com/watch?v=fogehnFNDw0&feature=relatedhttp://www.youtube.com/watch?v=lWDha0wqbcI&feature=relatedhttp://www.youtube.com/watch?v=lWDha0wqbcI&feature=relatedhttp://www.youtube.com/watch?v=lWDha0wqbcI&feature=relatedhttp://www.youtube.com/watch?v=lWDha0wqbcI&feature=relatedhttp://www.youtube.com/watch?v=fogehnFNDw0&feature=relatedhttp://www.youtube.com/watch?v=fogehnFNDw0&feature=relatedhttp://www.youtube.com/watch?v=eiHWHT_8WrEhttp://www.youtube.com/watch?v=eiHWHT_8WrE


9/15

What about the AREA of a circle?

2r

2rr

First consider a square

The area of this square

in terms of r is

A= 2r x2r = 4r2


10/15

What about the AREA of a circle?

2r

2r

Now consider a circle inside the square

The area of the circle must be less thanthe area of the square

A < 4r2r

Area = ? xr2


11/15

Finding a

formulae for thearea of a circle


12/15

C= d or C=2r

Semi-circle=

r

r

r


13/15

Area of Rectangle= Base x Height

Area = r x r

Area =r2


14/15

The Area and Perimeter of a CircleA circle is defined by its diameter or radius

Diameter

The perimeter or circumference of a circle

is the distance around the outside

The area of a circle is the space inside it

The ratio of (pi)diameter

ncecircumfere

is an irrational number whose value to 15 decimal places is

= 3.14159265358979.... We usually say 3.14

The circumference is foundusing the formula

C=

d or C= 2

r (since d=2r)

The area is foundusing the formula

A=

r2


15/15

The Area and Perimeter of a CircleA circle is defined by its diameter or radius

Diameter

The perimeter or circumference of a circle

is the distance around the outside

The area of a circle is the space inside it

The ratio of (pi)diameter

ncecircumfere

is an irrational number whose value to 15 decimal places is

= 3.14159265358979.... We usually say 3.14

The circumference is foundusing the formula

C=

d or C= 2

r (since d=2r)

The area is foundusing the formula

C=

r2

circumference and area

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