Question

A horse is tied to a post by rope. If the horse moves along a circular path always keeping the rope tight and covers a distance of $110\text{m}$ while tracing ${56}^{\circ }$ at the center, the length of the rope will be:
(take $\pi =22/7)$

• A. $105\text{m}$
• B. $112.5\text{m}$
• C. $122.5\text{m}$
• D. $132\text{m}$

Answer 1

The correct option is B $112.5\text{m}$

Given:
Length of the arc travelled by the horse$\left(l\right)$ $=110\text{m}$
Angle traced $\left(\alpha \right)={56}^{\circ }$
Now, using the relation:
$l=\frac{\alpha }{{360}^{\circ }}\times 2\pi r$
Where $r$ is the radius of circle,
$\Rightarrow 110=\frac{{56}^{\circ }}{{360}^{\circ }}\times 2\times \frac{22}{7}\times r$

$\Rightarrow r=112.5\text{m}$