Unformatted text preview: The Circle
S5 Int 1 www.mathsrevision.com Main Parts of a Circle Investigation of the Ratio of Circle Circumference of the circle Composite shapes Perimeter Starter Questions
S5 Int 1 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 Parts of a Circle
S5 Int 1 Learning Intention Success Criteria 1. Know the terms circumference, diameter 2. 3. using Identify them on a Calculate the formula. www.mathsrevision.com 1. To revise the basics of the circle. and radius. circle. circumference 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Main part of a Circle
S5 Int 1 www.mathsrevision.com Main parts of the circle
1 r = D 2 O D = 2r
Monday 13 February 2012 Created by Mr Lafferty 4 Main part of a Circle
S5 Int 1 www.mathsrevision.com 2cm cm 10 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
S5 Int 1 www.mathsrevision.com Now try Ex Int 1 TJ Book 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
S5 Int 1 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
S5 Int 1 "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
S5 Int 1 75 years old www.mathsrevision.com The Greek mathematician Archimedes of Syracuse (287 212 BC) who flourished in Sicily is S5 Int 1ly 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. Monday 13 February 2012 Created by Mr Lafferty 9 Parts of the Circle
S5 Int 1 Circumference 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
S5 Int 1 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
S5 Int 1 Our Investigation
www.mathsrevision.com
O To find a relationship between the diameter and circumference of a given circle. How can we measure the diameter and circumference
Monday 13 February 2012 Created by Mr Lafferty Question ? 12 Measuring the Diameter S5 Int 1 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 S5 Int 1 of a circle www.mathsrevision.com O 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
S5 Int 1 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
S5 Int 1
Circle I nvest igat ion
Circle 1
2 3 3 Cir cumf Circumf erence = C Calculat ions
C+D= 23. 1 20. 9 18. 8 16. 6 14. 7 12. 5 10. 5 8. 4 C D= 12. 1 10. 9 9. 8 8. 6 7. 7 6. 5 5. 5 4. 4 C/ D= 3. 2 3. 2 3. 2 3. 2 3. 2 3. 2 3. 2 3. 2 CxD= 96. 8 79. 5 64. 4 50. 4 39. 2 28. 5 20. 0 12. 8 5. 5
5. 0 Diamet er = D 17. 6
15. 9 14. 3
12. 6 4. 5
4. 0 4 5 5
6 6 7 7 8 8 11. 2
9. 5 9. 5 8. 0 8. 0 6. 4 6. 4 3. 5
3. 0 3. 0 2. 5 2. 5 2. 0 2. 0 Monday 13 February 2012 Created by Mr Lafferty 16 Circle Investigation
S5 Int 1 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 Pronounced C =D "Pi" C = circumference
D = diameter Monday 13 February 2012 Created by Mr Lafferty ; 3.14 17 Circle Investigation
S5 Int 1 www.mathsrevision.com No Exercise 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
S5 Int 1 1. N ame t his shape. www.mathsrevision.com 4
2 . C a lc ula t e ( 3 m ) x ( 4 m ) 3. Find t he mean, median and mode of dat a set
13 Feb 2012 3, 5, 5, 7, 10
Created by Mr. Lafferty Maths Dept. Main Parts of a Circle
S5 Int 1 Learning Intention Success Criteria 1. Know the terms circumference, diameter 2. 3. using Identify them on a Calculate the formula. www.mathsrevision.com 1. To revise the basics of the circle. and radius. circle. circumference 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Main Parts of a Circle
S5 Int 1 Main parts of the circle
www.mathsrevision.com
1 r = D 2 O C = D
13 Feb 2012 Circumference D = 2r
Created by Mr. Lafferty Maths Dept. S5 Int 1 Calculating the Circumference
Example : Find the length of the circumference (Perimeter) of each circle www.mathsrevision.com 2cm m 0c 1 C = D = 10
Created by Mr. Lafferty Maths Dept. D = 2r D = 4c m = 3 1.4 c m
13 Feb 2012 C = D = = 12 .5 6 c m 4 S5 Int 1 Calculating the Circumference
Q. Calculate the curved part of this shape.
Solution www.mathsrevision.com 6m
90
o C = D 1 c ur ve d le ng t h = D 4 1 c ur ve d le ng t h = 12 4 c ur ve d le ng t h = 3 Created by Mr Lafferty 23 c ur ve d le ng t h = 9 .4 m
Monday 13 February 2012 Main part of a Circle
S5 Int 1 www.mathsrevision.com Now try Ex Int 1 TJ Book 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
S5 Int 1 1. Find t he cir cumf er ence of t he cir cle.
4 www.mathsrevision.com 2. 3.
13 Feb 2012 Calculat e ( 7 ) x ( 12 ) 6 Find t he mean, median and mode of dat a set 6, 7, 3, 10, 8, 10, 12
Created by Mr. Lafferty Maths Dept. Composite Perimeter
S5 Int 1 Learning Intention Success Criteria 1. Recall knowledge of circles so far. 2. Solve mixed problems by applying all our knowledge so far. www.mathsrevision.com 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Composite Perimeter
S5 Int 1 Things to think about when doing exercise. www.mathsrevision.com 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 !
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Composite Perimeter
S5 Int 1 Q. Find the perimeter for the semicircle shape ? www.mathsrevision.com 1 P = D + 2 0 2
180
o Solution 1 P= 2 20 +20 P = 10 + 2 0
Monday 13 February 2012 Created by Mr Lafferty P = 5 1.4 c m 28 Composite Perimeter
S5 Int 1 Q. Find the perimeter of the shape below ? www.mathsrevision.com
8cm
90
o 1 P = D + 8 + 8 4 1 P = 16 + 8 + 8 4 P = 4 + 16 P = 2 8 .6 c m Solution Monday 13 February 2012 Created by Mr Lafferty 29 Composite Perimeter
S5 Int 1 Example 1 : Find the perimeter of this shape Perimeter = 3 sides + semicircle www.mathsrevision.com 1 P = 5 + 20 + 5 + 2
5 cm 20 P = 30 + 10 P = 61.4cm
20cm
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Composite Perimeter
S5 Int 1 www.mathsrevision.com Now try Ex Int 1 TJ Book 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions
S5 Int 1 1. Find t he lengt h of t he cur ved par t . www.mathsrevision.com 2cm 2. 3.
13 Feb 2012 Calculat e 2 0 + 8 Simplif y 4 3(5y  2)
Created by Mr. Lafferty Maths Dept. Composite Area
S5 Int 1 Learning Intention Success Criteria 1. Recall knowledge of circles so far. 2. Solve mixed problems by applying all our knowledge so far. www.mathsrevision.com 1. To give some examples of problems that we can solve by applying our knowledge of circles and of the course so far. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Composite Area
S5 Int 1 Example 1 : Find the area of the shape Area = rectangle + semicircle www.mathsrevision.com 1 2 A=l b + r 2
5 cm 20cm
13 Feb 2012 1 2 A = 20 5 + ( 10) 2 A = 100 + 157 A = 257 cm 2
Created by Mr. Lafferty Maths Dept. Composite Area
S5 Int 1 Example 1 : Find the area of the red part. www.mathsrevision.com Area = Big Circle Small Circle
4cm A = r 2 B
2  r 2 S A= 5  A = 21
A = 66 cm 2
Created by Mr. Lafferty Maths Dept. 2 2 10cm
13 Feb 2012 Composite Area
S5 Int 1 Example 2 : A circle is contained in a square. Find the grey shaded area below.
Area = square circle www.mathsrevision.com 8cm A=l 2 r 2 A = 8 8 ( 4) 2 A = 64  50.24 A = 13.76 cm 2
13 Feb 2012 Created by Mr. Lafferty Maths Dept. Composite Area
S5 Int 1 www.mathsrevision.com Now try Ex Int 1 TJ Book 13 Feb 2012 Created by Mr. Lafferty Maths Dept. ...
View
Full Document
 Spring '10
 Archimedes, Mr. Lafferty Maths Dept, Lafferty Maths Dept, Mr. Lafferty Maths

Click to edit the document details