Question

A piece of wire 20 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

Arc is a part of circle that makes 60° between radii at endpoints A and B of wire.

So, it form the shape of a sector.

r = ? l = 20 cm

∴ Length of arc l = `(2 pir theta)/360^circ`

⇒ 20 cm = `(2 xx pi xx r xx 60^circ)/360^circ`

⇒ `2pir = 20 xx 6`

⇒ r = `120/(2pi) = 60/pi ` cm