Question

Find the length of an arc of a circle of radius 14 cm which subtends an angle of 36° at the centre.

Answer 1

Angle in radians = Angle in degrees × \(\frac{\pi}{180}\)

Angle in radians = Angle in degrees x \(\frac{\pi}{180}\)

θ = 1/r Where θ is central angle, L = length of arc, r = radius

Therefore angle = 36 x \(\frac{\pi}{180}\) = \(\frac{\pi}{5}\)

Now

l = r x θ

= 14 x \(\frac{\pi}{5}\) = 14 x \(\frac{22}{35}\) = \(\frac{44}{5}\) = 8.8

Therefore the length of the arc is 8.8 cm