3. Name these Features The distance from the centre to the edge The distance from one side to the other passing through the centre The distance all of the way round the edge The blue line Area Circumference Rotation Radius Degree Chord Sector Segment Diameter Sphere Concentric Arc
4. The distance from the centre to the edge RADIUS The distance from one side to the other passing through the centre DIAMETER The distance all of the way round the edge CIRCUMFERENCE The blue line CHORD Where can you see i) a segment ii) a sector iii) an arc? Sector Segment An ARC is the name for part of the circumference
11. Diameter = 12 cm C = d C = 3.14 X 12 C = 37.68 How to calculate the circumference The symbol is the Greek letter pi. It stands for a number that can never be found exactly. It is approximately 3.14 Evaluate the CIRCUMFERENCE Always, write the formula (rule )
12. Diameter = ?cm C = d d = C ÷ d = C ÷ 3.14 d = 40 ÷ 3.14 d = 12.73 How to calculate the diameter from the circumference If the circumference is 40 cm. evaluate the DIAMETER Always, write the formula (rule )
13. Remember d = 2 X r r = d ÷ 2 Diameter Radius Circumference 1 24 2 14 3 17 4 30 5 22 6 120 7 78 8 88 9 120 10 340
16. 72 0 A B How to Calculate an Arc Length Calculate the arc length AB for a circle with a diameter of 12 cm . Circumference C = 3.14 x 12 C = 37.6 cm But we only want the arc length AB. This is 72 0 of the circle and because there are 360 0 in a circle, this is 72 ÷ 360 = 0.2 as a decimal fraction of the circumference AB = 0.2 x C AB = 0.2 x 37.6 AB = 5.52
17. x 0 A B The FORMULA for an Arc Length Calculate the arc length AB for a circle with a diameter of d AB = x/360( d) AB = (x ÷ 360) x 3.14 x d Divide the arc length’s angle by 360 then multiply this by the circumference
18. x 0 A B Using the FORMULA for an Arc Calculate the arc length AB for these circles AB = x/360( d) AB = (x ÷ 360) x 3.14 x d X 0 Diam Arc AB X 0 Diam Arc AB 1. 144 12 4. 270 60 2. 48 40 5. 24 36 3. 180 25 6. 70 40
19. x 0 A B Using the FORMULA for an Arc Calculate the arc length AB for these circles AB = x/360( d) AB = (x ÷ 360) x 3.14 x d X 0 Diam Arc AB X 0 Diam Arc AB 1. 144 12 15.07 4. 270 60 141.3 2. 48 40 20.10 5. 24 36 7.54 3. 180 25 39.25 6. 70 40 24.42
20. Finding the Number of Revolutions (turns) of a Wheel on a Journey Level 8
21. A wheel with a spot of blue paint The wheel turns once This distance is the circumference When a wheel makes one complete revolution, the distance that it travels is its circumference
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24. Wheel’s Diameter Circumference Distance of Journey Number of Revolutions 0.3 metres 120 metres 0.4 metres 200 metres 0.7 metres 150 metres 0.6 metres 1000 metres
25. A car’s wheels have a diameter of 45 cm. How many times will the wheel revolve during a journey of 100 km? Level 8 A bike’s wheels have a diameter of 70 cm. How many times will the wheel revolve during a journey of 50 km?