A chord of a circle of radius 14 cm


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A chord AB of a circle, of radius 14 cm makes an angle of 60° at the centre of the circle. Find the area of the minor segment of the circle. (Use )

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Answer:

The area of the minor segment is 17.80 cm².

Step-by-step explanation:

Given :

Radius of a circle,r = 14 cm  

Angle at the centre of a circle, θ = 60°

Area of the minor segment ,A = {πθ/360 - sin θ /2 cos θ/2 }r²

A = {60°π/360° - sin 60°/2 cos 60°/2 }× 14²

A = {π/6  - sin 30°cos 30°} × 196

A = {π/6  - 1/2 × √3/2} × 196

A = {π/6  - √3/4 } × 196

A = {196π/6 - 196 × √3/4}

A = {196 × 22/7× 1/6 - 196 × 1.732 × 1/4}

[√3 = 1.732]

A = 102.66 - 84.68

A = 17.80 cm²

Area of the minor segment = 17.80 cm²

Hence, the area of the minor segment is 17.80 cm².

HOPE THIS ANSWER WILL HELP YOU….


Here are more questions of the same chapter :

A chord 10 cm long is drawn in a circle whose radius is 5√2 cm. Find area of both the segments.

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A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.

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