Question

An arc subtends an angle of 90° at the centre of the circle of the radius 14 cm. Write the area of minor sector thus formed in terms of π.

Answer 1

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

`r=14 cm`

`θ=90°`

Now we will find the area of the minor sector.

Area of the minor sector =`θ/360xxpir^2`

Substituting the values we get, 

Area of the minor sector = `90/360xxpixx14^2`.......(1)

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

Area of the minor sector `=1/4xxpixx14^2`

`"Area of the minor sector" =1/4xxpixx14xx14`

`"Area of the minor sector" =pixx7xx7`

Area of the minor sector = `49 pi`

Therefore, area of the minor sector is `49 pi cm^2`