The Circle

1. The Circle Main Parts of a Circle Investigation of the Ratio of Circle Circumference of the circle Composite shapes Perimeter Diameter = Circumference ÷π Area of a circle Composite Area

2. Starter Questions 7cm Created by Mr Lafferty

3. Main Parts of a Circle Learning Intention Success Criteria • To revise the basics of the circle. • 1. Know the terms circumference, diameter and radius. • 2. Identify them on a circle. • 3. Calculate the circumference using formula. Created by Mr. Lafferty Maths Dept.

4. radius Diameter Circumference Main part of a Circle Main parts of the circle O Created by Mr Lafferty

5. Main part of a Circle 2cm 10cm Created by Mr Lafferty

6. Main part of a Circle Now try Exercise 1 Ch9 (page 100) Created by Mr. Lafferty Maths Dept.

7. Starter Questions 5cm Created by Mr Lafferty

8. Stars In Your Eyes “Today Matthew we are going to be” Archimedes of Syracuse Created by Mr Lafferty

9. History of Circles 75 years old The Greek mathematician Archimedes of Syracuse (287- 212 BC) who flourished in Sicily is generally considered to be the greatest mathematician of ancient times. He is credited with determining the relationship between the diameter and the circumference of a circle. This was first recorded by Archimedes in the book Measurement of a Circle (225 BC). In this investigation we are going to attempt to follow Archimedes steps and arrive at the equation for determining the circumference for any given circle. Created by Mr Lafferty

10. The radius is measured from the centre of the circle to the edge. Circumference radius diameter The diameter is measured from one edge to the other passing through the centre of the circle. Parts of the Circle O O = centre of circle Created by Mr Lafferty

11. Circle Investigation • Construct a table shown below to enable us • to record our results. Created by Mr Lafferty

12. O Investigation of the Circle Our Investigation To find a relationship between the diameter and circumference of a given circle. Question ? How can we measure the diameter and circumference Created by Mr Lafferty

13. O Use a ruler Measuring the Diameter of a circle O The diameter is the largest distance between one side of a circle to the other passing through the centre O. Created by Mr Lafferty

14. O Flexible tape measure Take a tape measure and put it round the circle Read off the measurement Measuring the Circumference of a circle Created by Mr Lafferty

15. End point Starting point Measuring the Circumference of a circle Roll along an even surface One complete rotation equals the length of the circumference Be careful to avoid slip! Created by Mr Lafferty

16. Circle Investigation Created by Mr Lafferty

17. Circle Investigation • Using your results write down, in your own words, • an approximate relationship between the • circumference and diameter for a given circle. “Circumference approximately equals three and bit diameters” Actual value is 3.14 which we write as π Pronounced “Pi” Created by Mr Lafferty

18. Circle Investigation No Exercise Created by Mr. Lafferty Maths Dept.

19. Starter Questions 4 Created by Mr. Lafferty Maths Dept.

20. Main Parts of a Circle Learning Intention Success Criteria • To revise the basics of the circle. • 1. Know the terms circumference, diameter and radius. • 2. Identify them on a circle. • 3. Calculate the circumference using formula. Created by Mr. Lafferty Maths Dept.

21. radius Diameter Circumference Main Parts of a Circle Main parts of the circle O Created by Mr. Lafferty Maths Dept.

22. Calculating the Circumference Example : Find the length of the circumference (Perimeter) of each circle 2cm 10cm Created by Mr. Lafferty Maths Dept.

23. Solution Calculating the Circumference Q. Calculate the curved part of this shape. 6m 90o Created by Mr Lafferty

24. Main part of a Circle Now try Exercise 2 Ch9 (page 100) Created by Mr. Lafferty Maths Dept.

25. Starter Questions 4 Created by Mr. Lafferty Maths Dept.

26. Composite Perimeter Learning Intention Success Criteria • Recall knowledge of circles so far. • 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far. • 2. Solve mixed problems by applying all our knowledge so far. Created by Mr. Lafferty Maths Dept.

27. Composite Perimeter Things to think about when doing exercise. The perimeter of a semicircle ……. Find whole circle then half it ! The perimeter of a quarter circle ……. Find whole circle then quarter it ! Composite perimeter ……. Find each perimeter and add them together ! Created by Mr. Lafferty Maths Dept.

28. Composite Perimeter Q. Find the perimeter for the semi-circle shape ? Solution 180o Created by Mr Lafferty

29. Solution Composite Perimeter Q. Find the perimeter of the shape below ? 8cm 90o Created by Mr Lafferty

30. 5 cm 20cm Composite Perimeter Example 1 : Find the perimeter of this shape Perimeter = 3 sides + semicircle Created by Mr. Lafferty Maths Dept.

31. Composite Perimeter Now try Extension Booklet 6E (page 125) Created by Mr. Lafferty Maths Dept.

32. Starter Questions Created by Mr. Lafferty Maths Dept.

33. Finding the Diameter The Circle Learning Intention Success Criteria • Understand how to rearrange circumference formula to find diameter. • 1. To explain how we can find diameter of a circle if we know the circumference. • 2. Solve diameter problems. Created by Mr. Lafferty Maths Dept.

34. Finding the Diameter The Circle We can easily rearrange the circumference formula so that we have the diameter D on one side. You have 1 minute to rearrange equation. Remember change side change sign Created by Mr. Lafferty Maths Dept.

35. Finding the Diameter The Circle Example : Find the diameter of each circle given the circumference. C = 62.8 cm C =15.7 cm 5cm 20cm Created by Mr. Lafferty Maths Dept.

36. Finding the Diameter Now try Extension Booklet 4E (page 32) Created by Mr. Lafferty Maths Dept.

37. Starter Questions Created by Mr. Lafferty Maths Dept.

38. Area of a Circle Peeling an orange A circumference A B x x O O • What do we call the distance OA in terms of • the large circle. • What do we call the distance AB in terms of the large circle.

39. A B x O Area of a Circle • What is the formula for the area • of a right-angle triangle. • Use this formula to work out • the area for a circle. Created by Mr. Lafferty Maths Dept.

40. If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. 1 8 2 2 7 1 3 6 5 8 6 4 4 3 7 5 Area of a Circle Created by Mr Lafferty

41. If we cut the sectors Thinner and thinner then we get closer and closer to a rectangle. Hence we can represent the area of a circle by a rectangle. 8 6 4 2 3 7 1 5 thinner and thinner sectors Area of a Circle Created by Mr Lafferty

42. Area of a Circle But the area inside this rectangle is also the area of the circle Created by Mr Lafferty

43. Area of a circle Solution Q.Find the area of the circle ? 4cm Created by Mr. Lafferty Maths Dept.

44. The Area of a circle Solution • The area of a circle is 12.64 cm2. • Find its radius? Created by Mr Lafferty

45. Area of a circle Solution • The diameter of the circle is 60cm. • Find area of the circle? Created by Mr. Lafferty Maths Dept.

46. Area of a Circle Now try Extension booklet 5E (page 35) Created by Mr. Lafferty Maths Dept.

47. Starter Questions 2cm Created by Mr. Lafferty Maths Dept.

48. Composite Area Learning Intention Success Criteria • Recall knowledge of circles so far. • 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far. • 2. Solve mixed problems by applying all our knowledge so far. Created by Mr. Lafferty Maths Dept.

49. 5 cm 20cm Composite Area Example 1 : Find the area of the shape Area = rectangle + semicircle Created by Mr. Lafferty Maths Dept.

50. Composite Area Example 1 : Find the area of the red part. Area = Big Circle – Small Circle 4cm 10cm Created by Mr. Lafferty Maths Dept.