Question

A piece of wire 20 cm long is bent into the from 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 make `60^(@)` between radii at end points P and Q of wire. ltbgt So, it form the shape of a sector.
`r + ?, l = 20 cm`
`:.` Length of arc `l = (2 pi r theta)/(360^(@))`

`rArr = 20 cm = (2 xx pi xx r xx 60^(@))/(360^(@))`
`rArr 2pi r = 20 xx 6`
`rArr r = (120)(2 pi) = (60)/(pi) cm`
Hence, radius (r) `= (60)/(pi) cm`