Question

In figure 7.33 O is the centre of the sector. ∠ROQ = ∠MON = 60°. OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN. (π =22/7 )

Answer 1

We know,
Length of arc
$= \frac{\pi \times r \times \theta}{180 \degree}$
where theta = Angle of sector
r =radius of sector

1) Arc (RXQ) ,
OR = 7 CM
Angle of sector =
$60 \degree$

Length of arc =
$\frac{\pi \times 7 \times 60 \degree}{180 \degree} = \frac{7\pi}{ 3} cm$

2)Arc (MYN) :

Since, Angle of sector is constant .
And Length of sector is proportional to arc radius.
And, OM = 3 * OR = 21 cm
=> Lengtj of arc MYN
= 3* L arc ( RXQ)
= 3* 7π/3 = 7π cm