Class Activity - Circle
- 1. CIRCLE Prepared by : Pang Kai Yun, Sam Wei Yin, Ng Huoy Miin, Trace Gew Yee, Liew Poh Ka, Chong Jia Yi
- 2. CIRCLE A circle is a plain figure enclosed by a curved line, every point on which is equidistant from a point within, called the centre.
- 3. DEFINITION Circumference - The circumference of a circle is the perimeter Diameter - The diameter of a circle is longest distance across a circle. Radius - The radius of a circle is the distance from the center of the circle to the outside edge.
- 4. CIRCUMFERENCE C = 2πrC = πd * Where π = 3.142
- 5. EXAMPLE (CIRCUMFERENCE) C = πd = 3.142 x 6 cm = 18.85 cm C = 2πr = 2 x 3.142 x 4 cm = 25.14 cm
- 6. AREA OF CIRCLE * Where π = 3.142 A = πr2
- 7. EXAMPLE 1 (AREA OF CIRCLE) A = πr2 = 3.142 x 62 = 3.142 x 36 = 113.11 cm2
- 8. EXAMPLE 2 (AREA OF CIRCLE) A = πr2 = 3.142 x 42 = 3.142 x 16 = 50.27 cm2 r = 𝑑 2 = 8 2 = 4cm
- 9. ARC A portion of the circumference of a circle.
- 10. ARC LENGTH (DEGREE) 𝑙 𝑎= 𝑛 360 𝑜 2𝜋r * A circle is 360 𝑜
- 11. EXAMPLE 1 (ARC LENGTH) 𝑙 𝑎 = 𝑛 360 𝑜 2𝜋r = 45 𝑜 360 𝑜 x 2 x 3.142 x 12 = 1 8 x 75.41 = 9.43 cm
- 12. RADIAN The angle made by taking the radius and wrapping it along the edge of the circle.
- 13. FROM RADIAN TO DEGREE Degree = 180 𝑜 π x Radians Radians = π 180 𝑜 x Degree FROM DEGREE TO RADIAN
- 14. EXAMPLE (FROM RADIAN TO DEGREE) 1. π 3 rad = 180 𝑜 π x π 3 rad = 60 𝑜 2. 2π 3 rad = 180 𝑜 π x 2π 3 rad = 120 𝑜 3. 5π 4 rad = 180 𝑜 π x 5π 4 rad = 225 𝑜
- 15. EXAMPLE (FROM DEGREE TO RADIAN) 1. 30 𝑜 = π 180 𝑜 x 30 𝑜 = π 6 rad 3. 270 𝑜 = π 180 𝑜 x 270 𝑜 = 3π 2 rad 2. 150 𝑜 = π 180 𝑜 x 150 𝑜 = 5π 6 rad
- 16. ARC LENGTH (RADIAN) 𝑙 𝑎 = r θ * Where θ is radians
- 17. EXAMPLE 2 (ARC LENGTH) 𝑙 𝑎 = r θ = 4.16 cm x 2.5 rad = 10.4 cm
- 18. EXAMPLE 3 (ARC LENGTH) 𝑙 𝑎 = r θ = 10 cm x π 4 rad = 7.86 cm 𝑙 𝑎 = r θ = 25 cm x 0.8 rad = 20 cm
- 19. SECTOR A sector is the part of a circle enclosed by two radii of a circle and their intercepted arc.
- 20. AREA OF SECTOR (DEGREE) 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟 𝐴𝑟𝑒𝑎 𝑜𝑓 𝐶𝑖𝑟𝑐𝑙𝑒 = 𝐶𝑒𝑛𝑡𝑟𝑎𝑙 𝐴𝑛𝑔𝑙𝑒 360 𝑜 𝐴 𝜋𝑟2 = 𝑛 360 𝑜 A = 𝑛 360 𝑜 𝜋𝑟2 By propotion,
- 21. EXAMPLE 1 (AREA OF SECTOR) Area = 𝑛 360 𝑜 𝜋𝑟2 = 45 𝑜 360 𝑜 x 3.142 x 62 = 1 8 x 3.142 x 36 = 14.14 cm2
- 22. AREA OF SECTOR (RADIAN) 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟 𝐴𝑟𝑒𝑎 𝑜𝑓 𝐶𝑖𝑟𝑐𝑙𝑒 = 𝐶𝑒𝑛𝑡𝑟𝑎𝑙 𝐴𝑛𝑔𝑙𝑒 2𝜋 𝐴 𝜋𝑟2 = θ 2𝜋 A = θ 2𝜋 𝑥 𝜋𝑟2 A = 1 2 𝑟2 θ By propotion,
- 23. EXAMPLE 2 (AREA OF SECTOR) Area 5 cm O 1.4 rad 2 2 1 r 2 2 5.17 4.15 2 1 cm
- 24. SEGMENT The segment of a circle is the region bounded by a chord and the arc subtended by the chord.
- 25. AREA OF SEGMENT 2 2 1 r sin 2 1 2 r )sin( 2 1 2 r * Where θ is radians
- 26. EXAMPLE (AREA OF SEGMENT) Solution: (i) 𝑙 𝑎 = 8 cm 𝑙 𝑎 = r θ 8 = r θ 8 = 6 θ θ = 1.333 radians Ð AOB = 1.333 radians The above diagram shows a sector of a circle, with centre O and a radius 6 cm. The length of the arc AB is 8 cm. Find (i) Ð AOB (ii) the area of the shaded segment. (ii) the area of the shaded segment 1 2 𝑟2(θ - sin θ) = 1 2 (6)2(1.333 - sin 1.333) = 1 2 (36)(1.333 – 0.927) = 6.498 cm2
- 27. CHORD Chord of a circle is a line segment whose ends lie on the circle.
- 28. GIVEN THE RADIUS AND CENTRAL ANGLE Chord length = 2r sin θ 2
- 29. EXAMPLE 1 Chord length = 2r sin θ 2 = 2(6) sin 90 2 = 12 x sin 45 = 8.49 cm
- 30. GIVEN THE RADIUS AND DISTANCE TO CENTER This is a simple application of Pythagoras' Theorem. Chord length = 2 𝑟2 − 𝑑2
- 31. EXAMPLE 2 Find the chord of the circle where the radius measurement is about 8 cm that is 6 units from the middle. Solution: Chord length = 2 𝑟2 − 𝑑2 = 2 82 − 62 = 2 64 − 36 = 2 28 = 10.58 cm
- 32. SEMICIRCLE
- 33. PERIMETER OF A SEMICIRCLE Remember that the perimeter is the distance round the outside. A semicircle has two edges. One is half of a circumference and the other is a diameter So, the formula for the perimeter of a semicircle is: Perimeter = πr + 2r
- 34. EXAMPLE (PERIMETER) Perimeter = πr + 2r = (3.142) 8 2 + 8 = 20.56 cm
- 35. AREA OF A SEMICIRCLE A semicircle is just half of a circle. To find the area of a semicircle we just take half of the area of a circle. So, the formula for the area of a semicircle is: Area = 1 2 π𝑟2
- 36. EXAMPLE (AREA) Area = 1 2 π𝑟2 = 1 2 x 3.142 x 42 = 25.14 cm2
- 37. SUMMARY
- 38. THANK YOU !