Question

The length of an arc (in cm) which subtended an angle 120° at the centre of the circle with r = 6 cm

Answer 1

The angle subtended at the centre of the circle is  90°  .

Step-by-step explanation:

Given :  

Length of the arc = 3π cm

Radius of a circle ,r = 6 cm

Length of the arc ,l = (θ/360°) × 2πr

3π = (θ/360°)× 2π ×6

3π =  (θ/360°) × 12π

3π /12 π =  (θ/360°)  

¼ =   (θ/360°)

4θ = 360°

θ = 360°/4

θ = 90°

Angle subtended at the centre of the circle = 90°  

Hence, the angle subtended at the centre of the circle is  90°  .

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