Relation between the area of sector and the length of an arc: Look at the following figure.

Here, O is the centre of the circle of radius r and APB is an arc of length l.

Clearly, measure of arc APB = Central angle = θ

Let the area of sector OAPB be A.

Now, we have

From length of arc and area of corresponding sector, we can also conclude that.

here i understood the first part very clearly i.e. till area of setor=radius/2*length of arc

but i am not able to understand the second relation.

pls help me in understanding it.

HereGivenl=θ360×2πrθ360=l2πr----(1)andA=θ360×πr2θ360=Aπr2----(2)From (1) and (2) we getθ360=l2πr=Aπr2

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