Question

A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the radius of the circle.

Answer 1

Length, l = 22cm

θ = 60^∘

180^∘ = πrad

\(1° = \frac \pi {180}rad\)

\(60° = \frac \pi {180} \times 60 \,rad\)

\(= \frac \pi 3\, rad\)

Arc length = rθ

\(r = \frac 1\theta \)

\(=\frac {22}{\left(\frac \pi 3\right)}\)

\(= \frac{(22 \times 3)}{\left(\frac {22}7\right)}\)

r = 3 × 7

r = 21 cm

Answer 2

Length of arc = 22 cm