# The circumference and Area of a circle

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The circumference and Area of a circle http://hench-maths.wikispaces.com

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

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

http://illuminations.nctm.org/ActivityDetail.aspx?ID=116 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. Your goal is to discover the mystery number in the formulae by dividing the circumference by the diameter for each circle.

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 value of this mystery ratio?????

Early Attempts Egyptian Scribe Ahmes. in 1650 B.C. said C3.16049 x d ArchimedesArchimedes, said C 3.1419 x d Fibonacci. In 1220 A.D. said C3.1418xd What is the value of the number that multiplies the diameter to give the circumference????

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

An approximation to π π3.141592653589793238462643383279502884 19716939937510582097494459230781640628 62089986280348253421170679821480865132 82306647093844609550582231725359408128 48111745028410270193852110555964462294 89549303819644288109756659334461284756 48233786783165271201909145648566923460 34861045432664821339360726024914127372 45870066063155881748815209209628292540 91715364367892590360011330530548820466 521384146951941511609................forever….

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

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

Finding a formulae for the area of a circle

C= πd or C=2πr Semi-circle=πr πrπr r

Area of Rectangle= Base x Height Area = πr x r Area =πr 2

The Area and Perimeter of a Circle A circle is defined by its diameter or radius Diameter radius 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 π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π3.14 The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula A=πr 2

The Area and Perimeter of a Circle A circle is defined by its diameter or radius Diameter radius 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 π (pi) π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π3.14 The circumference is found using the formula C=π d or C= 2πr (since d=2r) The area is found using the formula C=πr 2

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