Question

A horse is tethered to a stoke by a rope $30m$ long. If the horse moves along the circumference of a circle always keeping the rope tight then how far it will have gone when the rope has traced an angle of ${105}^{\circ }$?

• A. $50m$
• B. $55m$
• C. $60m$
• D. $65m$

Answer 1

Answer: (B)

$55m$

The radius of the circle, $r=$ length of the rope $=30m$

Central angle, $\theta ={105}^{\circ }$

Distance covered by the horse along the circumference $=$ Length of the arc with ${105}^{\circ }$ as central angle

$=\frac{\theta }{{360}^{\circ }}\times 2\pi r=\frac{{105}^{\circ }}{{360}^{\circ }}\times 2\times \frac{22}{7}\times 30=55m$