Question

In a circle of radius 14cm, an arc subtends an angle of 30° at the centre, the length of the arc is

(a) 44 cm
(b) 28 cm
(c) 11 cm
(d) 22/3 cm​

Answer 1

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• In a circle of radius 14cm, an arc subtends an angle of 30° at the centre, the length of the arc is ?

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• Radius (r) = 14 cm
• Angle (θ) = 30°

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• Arc length (L) = ?

Here :)

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■ Arc length = Radius × Angle (In radian)

■ 30° in radians = π/60

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↬ Arc length (L) = Radius × Angle

↬ Arc length (L) = 14cm × π/60

↬ Arc length (L) = 22/30 cm ( Answer )

• Hope it helps

Answer 2

Solution :-

given that,

→ Radius of circle = 14 cm .

→ Angle at centre = 30°

we know that,

• 180° = π radian .

So,

→ 180° = π radian

→ 1° = (π/180) radian

→ 30° = (π/180) * 30 = (π/6) radian .

now, we know that, when angle at centre is in radian ,

• Length of arc = Angle at centre * Radius .

then,

→ Length of arc = (π/6) * 14

→ Length of arc = (22/7) * (1/6) * 14

→ Length of arc = (22 * 2)/6

→ Length of arc = (22/3) cm (D) (Ans.)

Hence, the length of the arc is equal to (22/3) cm .

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