Question

The length of an arc of a circle of radius 12cm is 10πcm. Find the central angle of this arc.

Answer 1

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Answer 2

The central angle of the arc is 150°

Given:

The length of an arc of a circle = 10πcm

Radius of the circle = 12 cm

To find:

The central angle of the arc

Solution:

Given radius r = 12 cm

Length of the arc = 10πcm

As we know the form for length of the arc = (θ/360°) 2πr  

Where θ is the central angle of the arc

⇒ From given data (θ/360°) 2πr  = 10π

⇒  (θ/360°) r  = 5

⇒  (θ/360°) 12= 5

⇒ (θ/30°) = 5  

⇒ θ =  30°× 5 = 150°  

The central angle of the arc = 150°

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