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In the Given Figure, 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 ) - Geometry

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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. ( \[\pi = \frac{22}{7}\]) 

 

Solution

In the given figure, ∠ROQ = ∠MON = θ = 60º
Radius of the sector ORXQ = OR = 7 cm 
∴ Length of the arc RXQ = \[\frac{\theta}{360º} \times 2\pi r = \frac{60º }{360º } \times 2 \times \frac{22}{7} \times 7\]  = 7.3 cm 

Radius of the sector OMYN = OM = 21 cm
∴ Length of the arc MYN = \[\frac{\theta}{360º } \times 2\pi r = \frac{60º }{360º } \times 2 \times \frac{22}{7} \times 7\]  = 22 cm

Thus, the lengths of the arc RXQ and arc MYN are 7.3 cm and 22 cm, respectively.

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 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 7: Mensuration
Practice set 7.3 | Q: 8 | Page no. 155
Solution In the Given Figure, 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 ) Concept: Perimeter and Area of a Circle.
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