Question

If the adjoining figure is a sector of a circle of radius 10.5 cm, what is the perimeter of the sector? (Take \[\pi = 22/7\]) 

 

Answer 1

Given figure is a quadrant of a circle. We have given radius of sector that is 10.5 cm. Arc AB subtended an angle of 60° at the centre of the circle.

Perimeter of the sector =`θ/360xx2pir+2r`

Substituting the values we get, 

`"Perimeter of the sector "=60/360xx2pixx10.5+2xx10.5` ..............(1) 

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

`"Perimeter of the sector"=1/6xx21pi+21`

Now we will substitute pi=`22/7`

`"Perimeter of the sector"=1/6xx21xx22/7+21`

`"Perimeter of the sector"=1/6xx3xx22+21`

`"Perimeter of the sector"=1/2xx22+21`

`"Perimeter of the sector"11+21`

`"Perimeter of the sector"=32`

Therefore, perimeter of the given sector is `32 cm`