Question

In the given figure, O is the centre of the sector. \[\angle\]ROQ =  \[\angle\]MON = 60^° . OR = 7 cm, and   OM = 21 cm. Find the lengths of  arc RXQ and arc MYN. (\[\pi = \frac{22}{7}\]) 

Answer 1

Given: ∠ROQ = ∠MON = 60°,

radius (r) = OR = 7 cm, radius (R) = OM = 21 cm 

To find: Lengths of arc RXQ and arc MYN.

i. Length of arc RXQ = `θ/360 xx 2π"r"`

`= 60/360 × 2 × 22/7 × 7`

`= 1/6 × 2 × 22`

= 7.33 cm

ii. Length of arc MYN = `θ/360 xx 2π"R"`

`= 60/360 × 2 × 22/7 × 21`

`= 1/6 × 2 × 22 × 3`

= 22 cm

∴ The lengths of arc RXQ and arc MYN are 7.33 cm and 22 cm respectively.