Question

Find, in terms of π, the length of the arc that subtends an angle of 30° at the centre of a circle of radius 4 cm.

Answer 1

Given, 

Angle = 30° 

Radius of circle = 4 cm 

180° = π radius 

1° = \(\frac{π}{180°}\)

30° = \(\frac{30°π}{180°}\) = \(\frac{π}{6}\) radius

Arc length = radius × angle subtended by arc at center

= 4 x \(\frac{π}{6}\) = \(\frac{2π}{3}\)