Question

In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of π? 

Answer 1

We have given the radius of the circle and angle subtended at the centre of the circle. 

`r=10 cm`

`θ=108°`

Now we will find the area of the sector.

Area of the sector=`θ/360 xxpir^2`

Substituting the values we get, 

Area of the sector=` 108/360xxpixx10^2` ...........(1)

Now we will simplify the equation (1) as below, 

Area of the sector =`3/10xxpixx100` 

Area of the sector =`3xxpixx10`

⇒ Area of the sector =`30 pi`

Therefore, area of the sector is`30 picm^2`