Area of a Circle

2,717 views

Published on

Published in: Education, Spiritual, Technology
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
2,717
On SlideShare
0
From Embeds
0
Number of Embeds
11
Actions
Shares
0
Downloads
102
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

Area of a Circle

  1. 1. The circumference and Area of a circle
  2. 2. What is the formula relating thecircumferenc e to the centre diameter? Diameter
  3. 3. C=?xdPeople knew that the circumference is about 3 times the diameter but they wanted to find out exactly. C≈3xd This means APPROXIMATELY EQUAL TO
  4. 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 bydividing the circumference by the diameter for each circle.If you measure and divide corectly you should always get the same valuefor the ratio circumference/diameter
  5. 5. The mystery ratio• What value did you find for the ratio? 3.1-3.2 is pretty good3.14 is very good and close to thetrue valueFor most circumstances we say Circumference ≈ 3.14 x diameterWhat is the true value of thismystery ratio?????
  6. 6. Early AttemptsEgyptian Scribe Ahmes. in 1650 B.C. said C≈3.16049 x dArchimedes, said C ≈3.1419 x dFibonacci. In 1220 A.D. said C≈3.1418xd What is the value of the number that multiplies the diameter to give the circumference????
  7. 7. The exact true value is……………UNKNOWN!!
  8. 8. An approximation to ππ≈3.141592653589793238462643383279502884 19716939937510582097494459230781640628 62089986280348253421170679821480865132 82306647093844609550582231725359408128 48111745028410270193852110555964462294 89549303819644288109756659334461284756 48233786783165271201909145648566923460 34861045432664821339360726024914127372 45870066063155881748815209209628292540 91715364367892590360011330530548820466 521384146951941511609................forever….
  9. 9. Videos on Circles•http://www.youtube.com/watch?v=eiHWHT_8WrE•A Rap about circleshttp://www.youtube.com/watch?v=fogehnFNDw0&feature=related•Circle Song2http://www.youtube.com/watch?v=lWDha0wqbcI&feature=related
  10. 10. What about the AREA of a circle? 2r First consider a square r The area of this square 2r in terms of r is A= 2r x2r = 4r2
  11. 11. 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 area of the square r 2r A < 4r2 Area = ? xr2
  12. 12. Finding aformulae for thearea of a circle
  13. 13. C= πd or C=2πr Semi-circle=πrπr r
  14. 14. Area of Rectangle= Base x Height Area = πr x r Area =πr2
  15. 15. The Area and Perimeter of a Circle A circle is defined by its diameter or 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 circumference The ratio of  π (pi) diameter π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The circumference is found The area is foundusing the formula using the formulaC=π d or C= 2πr (since d=2r) A=πr2
  16. 16. The Area and Perimeter of a Circle A circle is defined by its diameter or 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 circumference The ratio of  π (pi) diameter π is an irrational number whose value to 15 decimal places is π = 3.14159265358979.... We usually say π≈3.14The circumference is found The area is foundusing the formula using the formulaC=π d or C= 2πr (since d=2r) C=πr2

×