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A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the ripe stretched, covers 66 m and traces 120° at the centre, then find the length of the rope.

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A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the ripe stretched, covers 66 m and traces 120° at the centre, then find the length of the rope.
1). 30 m
2). 45 m
3). 31.5 m
4). 60 m


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1 answers

2 vote
Answered by on | Votes 2 |

Let the length of the rope be 'r'

The path is circular, and as the distance covered while tracing a complete 360o is 2πr, which is the circular path's circumference, the distance covered while tracing an angle of 120will be

(2πr/360o)×120o

=2πr/3

In the problem this distance is given to be 66m

Therefore, 2πr/3=66

⇒r=66×3/2π

=(66×3×7)/(22×2).................using (π=22/7)

=63/2

=31.5m

Therefore the length of the rope is 31.5m.

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