2. Circles & Circumference Standard Math

3. This is a circle.

4. A circle BACK

5. Many musical instruments have a circular surface. For example: Bingo Drum Tabla Snare Drum Bass Drum BACK

6. Five rings in the logo of Olympic games BACK A circle

7. Radius This is the radius of a circle. It is a line segment starting from the center of the circle. The radius of this circle is four inches. 4 in.

8. Diameter To find the length across the circle you would double the radius. 4 in.4 in The line segment that forms across is called the diameter. DIAMETER 4 in + 4 in = 8 in

9. Circumference To find the measurement all around the circle you would multiply the diameter by 3.14 or 3 for a good estimate!! Let’s Try!------------------->

10. Measuring Around the Circle Remember the radius is 4 inches. Double it to find the diameter. 4 in +4 in =8 in The best estimate of the length around the circle is 24 inches. 8 in x 3 in = 24 in 4 in 8 inches

11. Measuring Circles Review Radius Diamete r Circumferenc e Measurement ALL around the circle.

12. Find the diameter: 5 in. 3 in 7 in. 10 inches 6 inches 14 inches

13. Find the Circumference Length around the circle. 5 in. 3 in 7 in. 30 inches 18 inches 42 inches

14. ..

17. Circles A Circle is a set of points that are all the same distance from a given point, called the center or the origin. A circle is named by its origin. A radius of a circle is a line segment with one endpoint at the origin and the other endpoint on the circle.

18. Circles A chord is a line segment with both endpoints on the circle A diameter is a chord that passes through the origin of the circle.

19. Arc Part of a circle named by its endpoints Radius Line segment whose endpoints are the center of a circle and any point on the circle Diameter Line segment that passes through the center of a circle, and whose endpoints lie on the circle Chord Line segment whose endpoints are any two points on a circle

20. RadiusDiameterChordArc Semi Circle Centre O

21. RadiusDiameterChordArc Semi Circle Radius OM Centre M O

22. RadiusDiameterChordArc Semi Circle Centre E D Diameter DE O

23. RadiusDiameterChordArc Semi Circle Centre Chord PQ P Q O

24. RadiusDiameterChordArc Semi Circle Centre E G Arc PQR O F

25. RadiusDiameterChordArc Semi circle S Centre O Diameter Semicircle D E Semicircle DSE Semicircle

26. C 2 C U M F E R N C E A E I Down 1. The distance between any two points on the circumference of the circle. 2. The distance around the circle. 3. The distance from the centre of the circle to a point on the circle. R D I U S R 1 C 3 R A Across: 4. The line segment that joins any two points on the circle and passes through its centre. 5. A closed curve in a plane. 6. All points on the circle are equidistant from this point. 7. A line segment that joins any two points on a circle. 4 D A M TEE 5 I R LE 6 C E N T E H R O D 7

27. Name the parts of circle M. Additional Example 1: Identifying Parts of Circles O N P Q R M A. radii: B. diameters: C. chords: MN, MR, MQ, MO NR, QO NR, QO, QN, NP Radii is the plural form of radius. Reading Math

28. Name the parts of circle M. Check It Out! Example 1 A. radii: B. diameters: C. chords: GB, GA, GF, GD BF, AD A B C D E F G H AH, AB, CE, BF, AD

29. The circumference is the distance around a circle. Circumference Circumference is the perimeter of circles. Radius is half of the diameter. BACK

31. Find the Circumference of the circle. BACK

32. Find the circumference using the diameter. BACK

33. Find the circumference of the circle. You try this one. BACK

34. Area Of A Circle A = π r² 3.14 or ²²/ ₇ Example 1: A = π r² A = 3.14 ( 4 )² A = 3.14 ( 16 ) A = 50.24 in² 4 in

35. Example 2: A = π r² A = 3.14 ( 3 )² A = 3.14 ( 9 ) A = 28.26 cm² 6 cm

36. Example 1: Find the area of this circle 2  5 cm A =   r 2 =   2  5 2 = 19  6 cm 2 to 1 decimal place Key into your calculator:   2  5 and then press the [x 2 ] button

37. Example 2: Find the circumference of this circle 25  6 m A =   r 2 =   12  8 2 = 515 m 2 to the nearest whole number Here we know the diameter so we have to divide it by 2 to get the radius Radius = 25  6  2 = 12  8 m

38. The circumference is the distance around a circle. diameter 1230.1 What is the connection between the diameter and the circumference? circumference The symbol, , is said as pie, and is about 3.14 The connection between the circumference and the diameter is

39. Find the diameter of the circle below: How to find the diameter given the circumference If you have the circumference: divide the circumference by 3.14 (  ). State the formula Substitute the values for  and C.

40. Find the circumference of the circle below: How to find the radius given the circumference If you have the circumference: divide this by, , 3.14 first to get the diameter. State the formula Substitute the values for  and C. Then divide the diameter by 2.

41. Calculate the missing numbers in the table below using the circumference formula below. What’s the formula? 17.584 14.13 5 C (cm)d (cm)r (cm) Use 3.14 as an approximation for . 10 4.5 5.6 2.8 2.25 31.4

42. Plenary You should now be able to find the radius or diameter of a circle given the circumference. You should know and use the formula for the circumference of a circle. or Find the diameter of the circle below.

44. Circles & Circumference Standard Math BACK