S1_Level_E_Ch19_Circles

S1_Level_E_Ch19_Circles - Level E The Circle Main Parts of...

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Unformatted text preview: Level E The Circle Main Parts of a Circle Formula for Circumference www.mathsrevision.com Monday 13 February 2012 Created by Mr Lafferty 1 Starter Questions Level E 1. W hat shape has an inf int e line symmet ry. www.mathsrevision.com 2. Solve 3x+7 28. 3. Find t he perimet er of t he st ar. 4. Convert your answer t o Q3 t o (m). 7cm Monday 13 February 2012 Created by Mr Lafferty 2 Main part of a Circle Level E www.mathsrevision.com To identify the main parts of a circle. Learning Intention Success Criteria 1. 2. 3. Know the terms circumference, diameter and radius. Identify them on a circle. Calculate the circumference using formula. Monday 13 February 2012 Created by Mr Lafferty 3 Main part of a Circle Level E www.mathsrevision.com Main parts of the circle O 1 r = D 2 radius C = D Monday 13 February 2012 Circumference Diameter D = 2r Created by Mr Lafferty 4 Main part of a Circle Level E www.mathsrevision.com m 2c 10 c m 1 r = D r = 5c m 2 Monday 13 February 2012 Created by Mr Lafferty D = 2r D = 4c m 5 Main part of a Circle Level E www.mathsrevision.com Your turn Exercise 1 Chapter 19 Page 228 Monday 13 February 2012 Created by Mr Lafferty 6 Starter Questions Level E 1. The diamet er of a circle is 10cm. W hat is t he radius. www.mathsrevision.com 2. The radius of a circle is 3. 5cm. W hat is t he diamet er. 3. Find t he perimet er of t he st ar. 4. Convert your answer t o Q3 t o (mm). 5cm Monday 13 February 2012 Created by Mr Lafferty 7 Stars In Your Eyes Level E "Today Matthew we are going to be" www.mathsrevision.com Archimedes of Syracuse Monday 13 February 2012 Created by Mr Lafferty 8 History of Circles Level E www.mathsrevision.com 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. 75 years old 22931 years old Monday 13 February 2012 Created by Mr Lafferty 9 Parts of the Circle Circumference Level E The radius is measured from the centre of the circle to the edge. www.mathsrevision.com O radius O = centre of circle The diameter is measured from one edge to the other passing through the centre of the circle. diameter Monday 13 February 2012 Created by Mr Lafferty 10 Circle Investigation Level E Construct a table shown below to enable us to record our results. www.mathsrevision.com Circle I nvest igat ion Circle 1 2 3 4 5 6 7 8 Circumf erence = C Diamet er = D C+D= Calculat ions C- D= C/ D= CxD= Monday 13 February 2012 Created by Mr Lafferty 11 Investigation of the Circle Level E O Our Investigation To find a relationship between the diameter and circumference of a given circle. www.mathsrevision.com Question ? How can we measure the diameter and circumference Monday 13 February 2012 Created by Mr Lafferty 12 Measuring the Diameter Level E of a circle O O www.mathsrevision.com Use a ruler The diameter is the largest distance between one side of a circle to the other passing through the centre O. Monday 13 February 2012 Created by Mr Lafferty 13 Measuring the Circumference Level E of a circle O www.mathsrevision.com Flexible tape measure Take a tape measure and put it round the circle Read off the measurement Monday 13 February 2012 Created by Mr Lafferty 14 Measuring the Circumference of a circle Level E Roll along an even surface www.mathsrevision.com Starting point End point One complete rotation equals the length of the circumference Be careful to avoid slip! Monday 13 February 2012 Created by Mr Lafferty 15 Circle Investigation Level E Circle nvest igat ion nvest igat ion Circle II nvest igat ion Circle Cir cle Circle Circumf erence = C Cir cumf er ence = C erence C Circumf erence = C 17. 6 17. 6 17. 6 15. 9 15. 9 15. 9 14. 3 14. 3 12. 6 12. 6 11. 2 11. 2 11. 2 9. 5 9. 5 9. 5 Diamet er = D D Diamet er Diamet er ==D Diamet er = D 5. 5 5. 5. 5 5. 55 5. 0 5. 5. 00 5. 0 4. 5 4. 5 4. 4. 55 4. 4. 0 4. 00 4. 0 3. 3. 5 3. 55 3. 5 3. 3. 0 3. 00 3. 0 C+D= C+D= C+D= C+D= Calculat ions Calculat ions ions Calculat ions Calculat ions C- D= C- D= D= C- D= C- D= C/D= C/ D= D= C/C/D= C/D= CxD= CxD= CxD= CxD= CxD= CxD= www.mathsrevision.com 1 1 2 2 3 3 4 4 5 5 5 6 6 7 7 7 8 8 23. 1 20. 9 18. 8 16. 6 14. 7 12. 5 10. 5 8. 4 12. 1 10. 9 9. 8 8. 6 7. 7 6. 5 5. 5 4. 4 3. 2 3. 2 3. 2 3. 2 3. 2 3. 2 3. 2 3. 2 96. 8 79. 5 64. 4 50. 4 39. 2 28. 5 20. 0 12. 8 8. 0 8. 0 8. 0 6. 4 6. 4 2. 2. 5 2. 55 2. 0 2. 0 Monday 13 February 2012 Created by Mr Lafferty 16 Circle Investigation Level E www.mathsrevision.com Us ing y o ur re s ults write d o wn, in yo ur o wn wo rd s , a n a p p ro xim a te re la tio ns h ip b e twe e n th e c irc um fe re nc e a nd d ia m e te r fo r a g ive n c irc le . "C irc um fe re nc e a p p ro xim a te ly e q ua ls th re e a nd b it d ia m e te rs " Ac tua l va lue is 3 .1 4 wh ic h we write a s C =D P ro no unc e d "P i" C = circumference D = diameter ; 3.14 Monday 13 February 2012 Created by Mr Lafferty 17 Circle Investigation Level E www.mathsrevision.com Chapter 19 Exercise 2 Page 229 Q2 Monday 13 February 2012 Created by Mr Lafferty 18 ...
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