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

Answer:

The area of the minor sector is 49π cm².

Step-by-step explanation:

Given :  

Radius of a circle , r = 14 cm

Angle subtended by an Arc at the centre of a circle, θ = 90°

Area of the minor sector ,A =  θ/360° ×πr²

A = 90°/360° × π × 14²

A = ¼ × π × 196

A = 49π cm²

Area of the minor sector = 49π cm²

Hence, the area of the minor sector is 49π cm².

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Answer 2

Answer:

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

r=14cm

θθ=90°

Now we will find the area of the minor sector.

Area of the minor sector =

θ

θ360×πr2

Substituting the values we get,

Area of the minor sector =

90360×π×142.......(1)

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

Area of the minor sector

=14×π×142

Area of the minor sector=14×π×14×14

Area of the minor sector=π×7×7

Area of the minor sector = 49π

Therefore, area of the minor sector