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The circumference and Area of a circle

The circumference and Area of a circle. Circles. A circle is the set of all points in a plane that are the same distance from a given point, called the center. Circles. The circumference (C) is the distance around a circle.

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The circumference and Area of a circle

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  1. The circumference and Area of a circle

  2. Circles • A circle is the set of all points in a plane that are the same distance from a given point, called the center.

  3. Circles The circumference (C) is the distance around a circle. The diameter (d) is the distance across a circle through the center of the circle. The radius (r) is the distance from the center to any point on the circle.

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

  5. 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

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

  7. An approximation to π π≈3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609................forever….

  8. A circle is defined by its diameter or radius The Area and Perimeter of a Circle The perimeter or circumference of a circle is the distance around the outside radius The area of a circle is the space inside it Diameter The ratio of π (pi) 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

  9. A circle is defined by its diameter or radius The Area and Perimeter of a Circle The perimeter or circumference of a circle is the distance around the outside radius The area of a circle is the space inside it Diameter The ratio of π (pi) 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

  10. What about the AREA of a circle? 2r 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 are of the square A < 4r2 2r r 2r Area = ? xr2

  12. Finding a formula 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

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