Question

A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes $44\, metres$, when it has traced out $72^\circ$ at the centre, the length of the rope is

• A. $35\, metres$
• B. $22\, metres$
• C. $56\, metres$
• D. $45\, metres$

Answer 1

Answer: (A)

$35\, metres$

Answer 2

Length of arc $=2 \pi r \times \frac{\theta}{360^{\circ}}$
$\Rightarrow \,\,\,\,\,44=2 \times \frac{22}{7} \times r \times \frac{72}{360}$
$\Rightarrow \,\,\,\,\,r=\frac{44 \times 7 \times 5}{44}=35\, m$
which is the length of the rope.