SUBTOPIC 8.3:SUBTOPIC 8.3:AREA OF SECTOR OF A AREA OF SECTOR OF A

CIRCLECIRCLE

SUBTOPIC 8.3:SUBTOPIC 8.3:AREA OF SECTOR OF A AREA OF SECTOR OF A

CIRCLECIRCLE

CHAPTER 8: CHAPTER 8: CIRCULAR MEASURECIRCULAR MEASURE

The net of a cone consists of a circle and a sector.

Area of sector OPQRArea of circle

2

22

r

A

2

2rA

2

2

1rA

AREA OF A SECTORThe area of a sector, A is proportional to the angle

subtended at the centre of the circle.

PR

rO

Q

θ rad

Therefore,

The area of sector of a circle is;

22

1rA

When using the formula , remember that the angle θ is measured in radians.

22

1r

Example 1

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.

5 cm

O

1.4 rad

Solution

Area of the shaded sector 2

2

1r

2

2

5.17

4.152

1

cm

Example 2

Given the area of the shaded sector of a circle is 64 cm2 and the angle subtended at the centre is 120º. Calculate the radius of the circle.

r

O

120º

Solution

Area of the shaded sector

2

2

1r

094.22

164 2r

cmr

r

818.7094.2

2642

120º = 2.094

rad

Example 3

Given that the area of the shaded sector of a circle is 80 cm2 and the radius is 6.5 cm. Find the central angle, θ, in radian.

6.5 cm

O

θ

Solution

Area of the sector 2

2

1r

rad787.3

5.6

8022

25.62

180

WORKSHEET

1. Given a circle with centre O and radius 14 cm. The minor arc AB subtends an angle of 65º at the centre of the circle. Calculate the area of the minor sector subtended by the arc AB.

2. Complete the table below, given the areas and the radii of the sectors and angles subtended.

Area of sector, A Radius, r Angle subtended, θ

90 cm2 9.15 cm

38.12 cm 50º

72 cm2 θ = 1.64 rad

18л cm2 6.5 cm

200 cm2 1.778 rad

145 cm2 8 cm

SUMMARY

Circular Measure

Л rad = 180º

Area of sector, A

2

2

1rA

r

θ