#### Transcript The Circle 2 [PPS]

The Circle www.mathsrevision.com Level 3 Circumference of the circle Diameter = Circumference ÷ Area of a circle Fractions of a circle 21-Jul-15 Created by Mr. Lafferty Maths Dept. π Starter Questions Level 3 www.mathsrevision.com 1. A house appreciates by 20% in one year. If its initial price was £60 000. How much is it now. 2. Simplify the ratio 34 : 72 3. Tidy up the expression 15e + 3d +14d + 10e 5. 3cm Find the area of the shape. 21-Jul-15 Created by Mr. Lafferty Maths Dept. 6cm Main Parts of a Circle www.mathsrevision.com Level 3 Revision of 2 Learning Intention Success Criteria 1. To revise the basics of the circle. 21-Jul-15 1. Remember the terms circumference, diameter and radius. 2. Identify them on a circle. 3. Calculate the circumference using formula. Created by Mr. Lafferty Maths Dept. Main Parts of a Circle www.mathsrevision.com Level 3 Revision of 2 Main parts of the circle radius 1 r D 2 O Diameter Circumference D 2r C D 21-Jul-15 Created by Mr. Lafferty Maths Dept. Main part of a Circle www.mathsrevision.com Level 3 Revision of 2 Example : Find the length of the circumference (Perimeter) of each circle C D 10 31.4cm 21-Jul-15 D 2r D 4cm C D 4 12.56cm Created by Mr. Lafferty Maths Dept. Main part of a Circle www.mathsrevision.com Level 3 Revision of 2 Now try Exercise 1 Ch29 (page 118) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com Level 3 1. Find the area of the shape. 8 5 4 2. Calculate (-3m) x (-4m) 3. Find the mean, median and mode of data set 21-Jul-15 3,5,5,7,10 Created by Mr. Lafferty Maths Dept. Finding the Diameter The Circle www.mathsrevision.com Level 3 Learning Intention Success Criteria 1. We are learning we can find diameter of a circle if we know the circumference. 1. Understand how to rearrange circumference formula to find diameter. 2. Solve diameter problems. 21-Jul-15 Created by Mr. Lafferty Maths Dept. Finding the Diameter The Circle www.mathsrevision.com Level 3 We can easily rearrange the circumference formula so that we have the diameter D on one side. C D D 21-Jul-15 C Created by Mr. Lafferty Maths Dept. You have 1 minute to rearrange equation. Remember change side change sign Finding the Diameter The Circle Level 3 www.mathsrevision.com Example : Find the diameter of each circle given the circumference. C = 62.8 cm 21-Jul-15 C =15.7 cm C 62.8 D 20 cm C 15.7 D 5 cm Created by Mr. Lafferty Maths Dept. Finding the Diameter The Circle www.mathsrevision.com Level 3 Now try Exercise 2 Ch29 (page 121) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com Level 3 1. Find the area of the shape. 6 5 2. Calculate (5b) x (-4b) 3. Find the mean, median and mode of data set 21-Jul-15 4,8,7,7,8,10 Created by Mr. Lafferty Maths Dept. Area of a Circle Peeling an Levelorange 3 www.mathsrevision.com A x circumference r O A x 2 r B O circumference (2 r ) What do we call the distance OA in terms of the large circle. radius (r ) What do we call the distance AB in terms of the large circle. Area of a Circle www.mathsrevision.com Level 3 21-Jul-15 A r O 2 r x B What is the formula for the area of a right-angle triangle. 1 A base height 2 Use this formula to work out the area for a circle. 1 A r 2 r 2 A r2 Created by Mr. Lafferty Maths Dept. Area of a Circle www.mathsrevision.com Level 3 8 If we break the circle into equal sectors And lay them out side by side We get very close to a rectangle. 1 7 2 6 3 5 4 1 2 3 4 5 6 7 8 Demo Tuesday, 21 July 2015 Created by Mr Lafferty 15 Area of a Circle www.mathsrevision.com Level 3 1 2 3 4 5 6 7 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. 8 thinner and thinner sectors r r Tuesday, 21 July 2015 Created by Mr Lafferty 16 Area of a Circle www.mathsrevision.com Level 3 r r Area of a rectangle l b Area of a rectangle r r r 2 But the area inside this rectangle is also the area of the circle Area = πr2 Tuesday, 21 July 2015 Created by Mr Lafferty 17 Area of a circle Level 3 www.mathsrevision.com Q. Find the area of the circle ? Solution 4cm A r 2 A 4 2 A 50.26cm 2 21-Jul-15 Created by Mr. Lafferty Maths Dept. Area of a circle Level 3 www.mathsrevision.com Q. The diameter of the circle is 60cm. Find area of the circle? Solution A r 2 D 60 r 30cm 2 2 A 30 2 A 2826 cm 21-Jul-15 Created by Mr. Lafferty Maths Dept. 2 Area of a Circle www.mathsrevision.com Level 3 What have we learned so far Circumference D Area r 21-Jul-15 2 Created by Mr. Lafferty Maths Dept. Area of a Circle www.mathsrevision.com Level 3 Now try Exercise 3 Ch29 (page 123) 21-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions Level 3 www.mathsrevision.com 1. Find the area of the shape. 4 2. Calculate (-7) x (-12) 6 3. Find the mean, median and mode of data set 21-Jul-15 6,7,3,10,8,10,12 Created by Mr. Lafferty Maths Dept. Mixed Problems The Circle www.mathsrevision.com Level 3 Learning Intention Success Criteria 1. We are learning to solve problems by applying our knowledge of circles. 21-Jul-15 1. Recall knowledge of circles so far. 2. Solve mixed problems by applying all our knowledge so far. Created by Mr. Lafferty Maths Dept. Mixed Problems The Circle www.mathsrevision.com Level 3 Things to think about when doing exercise. 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 ! 21-Jul-15 Created by Mr. Lafferty Maths Dept. Mixed Problems The Circle Level 3 www.mathsrevision.com Example 1 : Find the area of the shape Area = rectangle + semicircle 1 2 A l b r 2 5 cm 20cm 21-Jul-15 1 2 A 20 5 (10) 2 A 100 157 A 257 cm2 Created by Mr. Lafferty Maths Dept. Mixed Problems The Circle www.mathsrevision.com Level 3 Example 2 : A circle is contained in a square. Find the grey shaded area below. 8cm Area = square - circle Al 2 - r 2 A 8 8 - (4)2 A 64 - 50.24 A 13.76 cm 2 21-Jul-15 Created by Mr. Lafferty Maths Dept. Mixed Problems The Circle www.mathsrevision.com Level 3 Now try Exercise 4 Ch29 (page 125) 21-Jul-15 Created by Mr. Lafferty Maths Dept.