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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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