2. Circumference of a Circle Parts of a circle Calculate d from r Calculate r from d Introducing pi Using C =π d C from d …. 5 circles C given radius 5 questions C from r …. 5 circles 5 questions C given radius or diameter ( 5 circles) 5 questions Distance round a window

3. Circumference Learning Intention To identify the main parts of a circle. Success Criteria 1.Know the terms circumference, diameter and radius. 2.Identify them on a circle. 3.Calculate the circumference using formula.

4. Main Parts of a circle O Circumference C i r c u m f e r e n c e The curved distance around the edge of a circle is called the curcumference O marks the centre of the circle ALL the points on the circumference are the same distance from the centre A line from the centre to the circumference is called the radius The diameter of a circle splits the circle in two radius diameter The diameter is the largest distance between two points on the circumference. The diameter passes through the centre of the circle

5. Know Radius. Find Diameter 3cm 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) The dashed line is also a radius of the circle 3 cm 6cm The diameter of a circle is twice its radius. Diameter = 2 x 3cm = 6cm 19.7 cm Radius = cm Diameter = = cm Next

6. Know Diameter. Find Radius 3cm 0 123 456 789 C. ÷ x 0 + On ² - Ans = √ (-) 3 cm 6cm The radius is half the diameter Radius = Diameter ÷ 2 Radius = 6 ÷ 2 = 3 cm 18.8 cm Diameter = cm Radius = = cm Next

7. Circumference of a circle The Greek mathematician Archimedes of Syracuse (287- 212 BC) who flourished in Sicily is generally considered to be the greatest mathematician of ancient times O Diameter He is credited with determining the relationship between the the circumference of a circle and its diameter Circumference No matter the size of the circle the CIRCUMFERENCE of the circle is roughly 3 times its DIAMETER CIRCUMFERENCE = 3 x DIAMETER

8. More Accuracy 3.141592653589793238462643383279502… Maths experts for years have been trying to get a more accurate answer to …. circumference ÷ diameter circumference ÷ diameter is roughly There isn’t an exact answer for this. It actually goes on forever! We’ll stop here since it would stretch for 600 miles if we printed them all! In 1989 a computer worked it out to 480 million decimal places. 3 CIRCUMFERENCE = 3 x DIAMETER means that

9. More Accuracy We can use a ruler to measure the diameter. How can we measure the circumference?

10. Measuring Circumference Measure length of label …or

11. …….. by rolling Roll along an even surface Be careful to avoid slip! Starting point End point

12. Checking it out Construct a table shown below to enable us to record our results. The previous slides demonstrated ways of measuring the diameter and the circumference Your answer should be close to 3

13. Another approach 3 8 15 C ÷ d Sides 2.6 5.20 3.06 3.31 3.12 3.19 Draw polygons inside a circle and outside a circle As the number of sides increase the shapes look more like a circle Divide the perimeter of polygon by the diameter of circle Answers approach the value of 3.14

14. Using Polygons Ancient Greeks were experts in drawing and manipulating shapes They would know how to draw regular polygons accurately Instead of using decimals they would use fractions One value he reached in his calculations was 22 7 7 = 22 ÷ 7 = 3.142857…….. The figures on the previous slide were determined using a computer

15. …. C ÷ d ….. by computer 3.141592653589793238462643383279502… There isn’t an exact answer We’ll stop here since it would stretch for 600 miles if we printed them all! In 1989 a computer worked it out to 480 million decimal places. It actually goes on forever!

16. More accurate measurement If it goes on for ever how can I write it down? We use the Greek letter instead. Mathematical Genius! This is called pi.

17. The Circumference When doing circle calculations on the calculator use =3.14 x diameter C = d C = 3.14 x d Circumference = C = 3 x diameter C = π x diameter Rough answers C =3.141592653589……. x diameter Accurate Answer

18. Circumference of a Circle C =π d 18.8 cm Next 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) C = x π d 3.14 18.8

19. C from d 5.4 18.2 14.4 16.8 01234 56789 3.14x C. ÷x 0 + On ² - Ans = √ (-) 9.6 Next Five π A C 3.14 Diameter r= d= r= d= r= d= r= d= r= d=

20. Circumference of a Circle from Diameter C =π d Next d = 3.4 d = 7.2 d = 14.6 d = 13.2 d = 8.6 C =π d = = = = = = = = = = 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) 3.14

21. Circumference of a Circle C =π d 8.6 cm Next C = Diameter= = Radius= 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) π 3.14 Calculate diameter 1st

22. C from r 8.6 9.4 6.2 2.3 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) 5.1 Next Five π A C 3.14 Radius r= d= r= d= r= d= r= d= r= d= = = = = =

23. Circumference of a Circle from r C =π d Next 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) r = 6.2 r = 4.7 r = 3.5 r = 8.3 r = 7.6 C =π d = = = = = = = = = = 3.14

24. C from d or r 7.3 8.7 2.5 10.8 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) 19 Next Five π A C 3.14 r OR d r= d= r= d= r= d= r= d= r= d=

25. Circumference of a Circle r or d C =π d Next 01234 56789 C. ÷x 0 + On ² - Ans = √ (-) d = 9.4 r = 3.4 d = 12.8 r = 8.2 d = 3 C =π d = = = = = 3.14 x 9.4 3.14 x 3 29.516 9.42 = = = = =

26. Perimeter of Circular Window 40 cm 60 cm Perimeter is round the edge  Know the following sides  60 cm  ? No rule for this but …… C =π d C =3.14 x 40 C =125.6 ÷2 D =125.6÷2 D =62.8 Perimeter =60 + 40 + 60 + 62.8 = 222.8

28. Find the Perimeter Four Semicircles round a square of side 14 cm The four semicircles can be made into TWO circles C= π

29. 0 123 456 789 9x6 C. ÷ x 54 + On ² - Ans = √ (-) 01234 56789 C. ÷x 0 + On ² - Ans = √ (-)