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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.
Solution
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`
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