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Y9 Booster

Y9 Booster. Lesson 10. Objectives – what you should be able to do by the end of the lesson. Use the formulae C = π d and A = πr² Solve problems involving circles. Use compasses to draw a circle. Label the centre, a radius, a diameter and a chord. radius. diameter. centre. chord.

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Y9 Booster

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  1. Y9 Booster Lesson 10

  2. Objectives – what you should be able to do by the end of the lesson • Use the formulae C = πd and A = πr² • Solve problems involving circles

  3. Use compasses to draw a circle. Label the centre, a radius, a diameter and a chord. radius diameter centre chord What is the longest chord you can draw? What is the name of the shape bounded by an arc and a diameter? What is the relationship between the radius and the diameter? Can you write the information in another way? Do you know any other relationships?

  4. Draw a circle using a pair of compasses. Measure its radius and circumference using a ruler. Measure its circumference using a piece of string. What is the relationship between diameter and circumference? The formula for the circumference of a circle is: C = 2 x π x r = 2πr or C = π x D = πD

  5. Consider a circle cut into sectors of equal sizes. Place the sectors side by side in a line. Half of them pointing down and the others pointing up. The resulting shape is almost a rectangle. h h = r w = 0.5 C = π X r w Area = r x π x r = πr²

  6. Circle problems M10.1 1 The London Eye has a diameter of 135 metres. How far do you travel in one revolution of the Eye? 2 A circle is drawn inside a 12 cm square so that it touches the sides. Calculate the shaded area.

  7. 1 The London Eye has a diameter of 135 metres. How far do you travel in one revolution of the Eye? What do we need to find? What is the formula for the circumference of a circle? Π x 135 m Distance in one revolution =

  8. 2A circle is drawn inside a 12 cm square so that it touches the sides. Calculate the shaded area. What is the area of the square? Remember to use radius What is the diameter of the circle? What is the formula for the area of a circle? What is the area of the circle? How can you find the area of the shaded part?

  9. The Round Table of King Arthur M10.2 At Winchester there is a large table known as the Round Table of King Arthur. The diameter of the table is 5.5 metres. (a) A book claims that 50 people sat around the table.Assume each person needs 45 cm around the circumference of the table.Is it possible for 50 people to sit around the table? (b) Assume people sitting around the table could reach only 1.5 metres.Calculate the area of the table that could be reached.

  10. Each person needs 45 cm of space What is the circumference of the circle? How many people can sit at the circumference IF they require 45 cm of space each? If each person can reach 1.5 m into the table the unshaded circle is the area where no-one can reach. How can you find its area? What is the area of the smaller circle? What is the shaded area?

  11. Objectives – how have we done? • Use the formulae C = πd and A = πr² • Solve problems involving circles

  12. Thank you for your attention

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