S2_Level_F_Ch29_Circles - The Circle Level F...

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Unformatted text preview: The Circle Level F www.mathsrevision.com Circumference of the circle Diameter = Circumference Area of a circle Fractions of a circle 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions Level F 1. A house appr eciat es by 20% in one year. I f it s init ial pr ice was 60 000. How much is it now. www.mathsrevision.com 2 . S im p lif y t h e r a t io 3 4 : 7 2 3. Tidy up t he expr ession 15e + 3d + 14d + 10e 5. Find t he ar ea of t he shape. Created by Mr. Lafferty Maths Dept. 3cm 6cm 13 Feb 2012 Main Parts of a Circle Level F Revision of Level E Learning Intention Success Criteria 1. Know the terms circumference, diameter and radius. 2. Identify them on a circle. www.mathsrevision.com 1. To revise the basics of the circle. 3. Calculate the circumference using formula. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Main Parts of a Circle Level F Revision of Level E Main parts of the circle www.mathsrevision.com O 1 r = D 2 radius C = D 13 Feb 2012 Circumference Diameter D = 2r Created by Mr. Lafferty Maths Dept. Main part of a Circle Level F Revision of Level E Example : Find the length of the circumference (Perimeter) of each circle 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 Main part of a Circle Level F Revision of Level E www.mathsrevision.com Now try Exercise 1 Ch29 (page 118) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions Level F 1. Find t he ar ea of t he shape. www.mathsrevision.com 8 5 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. Finding the Diameter Level F The Circle Learning Intention Success Criteria 1. Understand how to rearrange circumference formula to find diameter. 2. Solve diameter problems. www.mathsrevision.com 1. To explain how we can find diameter of a circle if we know the circumference. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Finding the Diameter Level F The Circle www.mathsrevision.com We can easily rearrange the circumference formula so that we have the diameter D on one side. C = D C D= 13 Feb 2012 Created by Mr. Lafferty Maths Dept. You have 1 minute to rearrange equation. Remember change side change sign Finding the Diameter Level F Example : Find the diameter of each circle given the circumference. C = 62.8 cm C =15.7 cm The Circle www.mathsrevision.com m 5c 20cm 13 Feb 2012 C 6 2 .8 D= = = 2 0 c m C 15 .7 D= = = 5 c m Created by Mr. Lafferty Maths Dept. Finding the Diameter Level F The Circle www.mathsrevision.com Now try Exercise 2 Ch29 (page 121) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions Level F 1. Find t he ar ea of t he shape. www.mathsrevision.com 6 5 2 . C a lc ula t e ( 5 b ) x ( 4 b ) 3. Find t he mean, median and mode of dat a set 13 Feb 2012 4, 8, 7, 7, 8, 10 Created by Mr. Lafferty Maths Dept. Peeling an orange Level F A x Area of a Circle circumference A x 2 r B www.mathsrevision.com r O O What do we call the distance OA in terms of the large circle. radius (r ) circle. What do we call the distance AB in terms of circumference (2 r ) the large Area of a Circle Level F A 2 r x B www.mathsrevision.com r O What is the formula for the area of a rightangle triangle. 1 A= base height 2 Use this formula to work out the area for a circle. 1 A= 2 r 2r A = r2 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Area of a Circle Level F www.mathsrevision.com 8 7 6 5 1 2 3 4 If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. 1 2 3 4 5 6 7 8 Monday 13 February 2012 Created by Mr Lafferty 15 Area of a Circle Level F www.mathsrevision.com 1 2 3 4 5 6 7 8 thinner and thinner sectors 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. r r Monday 13 February 2012 Created by Mr Lafferty 16 Area of a Circle Level F www.mathsrevision.com r r A r e a o f a r e c t ang le = l A r e a o f a r e c t ang le = r b r = r 2 17 2 But the area inside this rectangle is also the area of the circle A r e a o f a c ir c le = r Monday 13 February 2012 Created by Mr Lafferty Area of a circle Level F Q. Find the area of the circle ? Solution 4cm www.mathsrevision.com A = r A = 2 4 2 2 A = 5 0 .2 6 c m 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Area of a circle Level F Q. The diameter of the circle is 60cm. Find area of the circle? www.mathsrevision.com Solution D 60 r = = = 3 0c m 2 2 A = r 2 A = 30 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 2 2 A = 2 8 2 6 c m Area of a Circle Level F www.mathsrevision.com What have we learned so far Circumference = D Area =r 2 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Area of a Circle Level F www.mathsrevision.com Now try Exercise 3 Ch29 (page 123) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions Level F 1. Find t he ar ea of t he shape. www.mathsrevision.com 4 2 . C a lc ula t e ( 7 ) x ( 12 ) 3. 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. 13 Feb 2012 Mixed Problems Level F The Circle 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. Mixed Problems Level F The Circle Things to think about when doing exercise. www.mathsrevision.com The area of a semicircle ....... Find whole circle then half it ! The area of a quarter circle .......Find whole circle then quarter it ! Composite area .......Find each area and add them together ! 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Mixed Problems Level F The Circle 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. Mixed Problems Level F The Circle 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. Mixed Problems Level F The Circle www.mathsrevision.com Now try Exercise 4 Ch29 (page 125) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. ...
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