Question

In the given figure, O is the centre of the sector. $\angle ROQ=\angle MON={60}^o.$ OR = 7 cm, and OM = 21 cm. The sum of the lengths of arc RXQ and arc MYN is _____. (Use $\pi =\frac{22}{7}$ )

• A. 7.33 cm
  
• B. 22 cm
• C. 29.33 cm
• D. 36.66 cm

Answer 1

The correct option is C 29.33 cm

In the given figure, $\angle ROQ=\angle MON=\theta ={60}^o$

Radius of the sector ORXQ is OR $=7cm$

$\therefore$ Length of the arc RXQ
$=\frac{\theta }{360}\times 2\pi r$
$=\frac{60}{360}\times 2\times \frac{22}{7}\times 7$
$=7.33cm$

Radius of the sector OMYN is OM = $21cm$
$\therefore$ Length of the arc MYN
$=\frac{\theta }{360}\times 2\pi r$
$=\frac{60}{360}\times 2\times \frac{22}{7}\times 21$
$=22cm$

The sum of length of arc $RXQ$ and arc $MYN$ is 29.33 cm.