SUBTOPIC 8.3: AREA OF SECTOR OF A CIRCLE CHAPTER 8:  CIRCULAR MEASURE
The net of a cone consists of a circle and a sector.
Area of sector OPQR Area of circle AREA OF A SECTOR The area of a sector, A is proportional to the angle  subtended at the...
Therefore, The area of sector of a circle is; When using the formula   ,  remember that the  angle  θ  is measured  in rad...
Example 1 <ul><li>Calculate the area of the shaded sector of a circle of radius 5 cm. Given that the circle subtends an an...
Solution Area of the shaded sector
Example 2 <ul><li>Given the area of the shaded sector of a circle is 64 cm 2  and the angle subtended at the centre is 120...
Solution Area of the shaded  sector 120º = 2.094 rad
Example 3 <ul><li>Given that the area of the shaded sector of a circle is 80 cm 2  and the radius is 6.5 cm. Find the cent...
Solution Area of the sector
WORKSHEET
<ul><li>Given a circle with centre  O  and  </li></ul><ul><li>radius 14 cm. The minor arc  AB  subtends an angle of 65º at...
<ul><li>2. Complete the table below, given the areas and the radii of the sectors  </li></ul><ul><li>and angles subtended....
SUMMARY Circular Measure Л  rad = 180º Area of sector, A θ
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Add Math(F4) Circular Measure 8.3

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Add Math(F4) Circular Measure 8.3

  1. 1. SUBTOPIC 8.3: AREA OF SECTOR OF A CIRCLE CHAPTER 8: CIRCULAR MEASURE
  2. 2. The net of a cone consists of a circle and a sector.
  3. 3. Area of sector OPQR Area of circle AREA OF A SECTOR The area of a sector, A is proportional to the angle subtended at the centre of the circle. θ rad Q
  4. 4. Therefore, The area of sector of a circle is; When using the formula , remember that the angle θ is measured in radians.
  5. 5. Example 1 <ul><li>Calculate the area of the shaded sector of a circle of radius 5 cm. Given that the circle subtends an angle of 1.4 rad at the centre. </li></ul>1.4 rad
  6. 6. Solution Area of the shaded sector
  7. 7. Example 2 <ul><li>Given the area of the shaded sector of a circle is 64 cm 2 and the angle subtended at the centre is 120º. Calculate the radius of the circle. </li></ul>120 º
  8. 8. Solution Area of the shaded sector 120º = 2.094 rad
  9. 9. Example 3 <ul><li>Given that the area of the shaded sector of a circle is 80 cm 2 and the radius is 6.5 cm. Find the central angle, θ , in radian. </li></ul>θ
  10. 10. Solution Area of the sector
  11. 11. WORKSHEET
  12. 12. <ul><li>Given a circle with centre O and </li></ul><ul><li>radius 14 cm. The minor arc AB subtends an angle of 65º at the </li></ul><ul><li>centre of the circle. Calculate the </li></ul><ul><li>area of the minor sector subtended by the arc AB . </li></ul>
  13. 13. <ul><li>2. Complete the table below, given the areas and the radii of the sectors </li></ul><ul><li>and angles subtended. </li></ul>8 cm 145 cm 2 1.778 rad 200 cm 2 6.5 cm 18л cm 2 θ = 1.64 rad 72 cm 2 50º 38.12 cm 9.15 cm 90 cm 2 Angle subtended, θ Radius, r Area of sector, A
  14. 14. SUMMARY Circular Measure Л rad = 180º Area of sector, A θ
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