Question

AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by chord AB.

Answer 1

Answer:

Area of sector of a circle formed by chord AB = 8π/3 cm²

Step-by-step explanation:

Given :

Radius of circle,(OA,OB),r = 4 cm

Chord of a circle, AB = 4

Let ∠AOB = 2θ, Then, ∠AOL = ∠AOL = θ

In ∆OLA,

sin θ = Perpendicular /Hypotenuse  = AL/OA

sin θ = (4/2)/4 = 2/4 =  ½  

sin θ = ½  

sin θ = sin 30°

[sin 30°  = ½]

θ = 30°  

∠AOB = 2θ

∠AOB = 2 × 30° = 60°

∠AOB = 60°  

Area of the sector of a circle, AOB = (θ/360) × πr²

= (60°/360°) × π ×4²

= 1/6 × π × 16

= 8π/3 cm²

Area of sector of a circle, = 8π/3 cm²

Hence, Area of sector of a circle formed by chord AB = 8π/3 cm²

HOPE THIS ANSWER WILL HELP YOU….

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The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

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In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find  

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Answer 2

✨Answer:

Area of sector = 8π/3 cm^2.

✨Step-by-step explanation:

Since the chord AB = radius = 4cm

It will form an equilateral triangle AOB.

So,

Angle of sector = 60 degree

( Since all angles of equilateral triangle are 60 degree)

Now,

➡ Area of sector = theta /360° x πr^2

Area of sector = 60/360x π x 4^2

Area of sector = 1/6 x 16 x π

Area of sector = 8π/ 3 cm^2