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The circumference and Area of a circle

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

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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

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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.

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The mystery ratio 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?????

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Early Attempts Egyptian Scribe Ahmes. in 1650 B.C. said C x d ArchimedesArchimedes, said C 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????

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

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An approximation to π π forever….

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Videos on Circles _8WrEhttp://www.youtube.com/watch?v=eiHWHT _8WrE A Rap about circles Dw0&feature=related Circle Song2 qbcI&feature=related

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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

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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

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Finding a formulae for the area of a circle

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C= πd or C=2πr Semi-circle=πr πrπr r

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

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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 = 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

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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 = 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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