# Arc of a Circle

Concept

From our previous course on radian , we realise the radian = .We will need this information to find the arc of a circle. Let us look first at how to find the arc of a circle by using its radian.

Let us consider a circle with centre O and radius r.

We compare between the lengths and angles subtended of the arc and circle.

Hence the length of minor arc AB,

## Area of a Sector

We shall look at how to calculuate the area of a sector ,using radian and radius. The area of a sector is also directly proportional to the angle within the sector.

Example

Before the start of doing or looking through any of these questions, it would be good to draw labelled diagrams to give you a better understanding.

a) The radius of a circle with centre O is 5cm and the sector AOB subtends an angle of 2 radians. What is the length of its arc AB?

= 5(2) = 10 cm

The length of arc AB is 10 cm.

b) The circle with centre O has radius 3 cm and the angle which sector COD subtends is . Find the area of sector COD.

Remembering the formula for area of sector of a circle ,

A =

=

= 18cm

'Try it Out Yourself' Section

Figure out the area and arc of a circle's sector by trying the below exercises.

a) The length of arc AB is 12cm . Given that the centre is at O and that the radius of OA is 6cm , find the radian OAB.

b) The circle with centre O has radius 4 cm and the angle which sector COD subtends is . Find the area of sector COD.