Q65 / 180 · KCET 2009 · Mathematics

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 $44 \mathrm{~m}$, when it has traced out $72^{\circ}$ at the centre, the length of the rope is

  • A
    $22 \mathrm{~m}$
  • B
    $56 \mathrm{~m}$
  • C
    $45 \mathrm{~m}$
  • Correct answer
    D
    $35 \mathrm{~m}$

Solution

$$ \begin{aligned} &\text { Length of arc }=2 \pi \mathrm{r} \times \frac{\theta}{360^{\circ}} \\ &\Rightarrow \quad 44=2 \times \frac{22}{7} \times \mathrm{r} \times \frac{72}{360} \\ &\Rightarrow \quad \mathrm{r}=\frac{44 \times 7 \times 5}{44}=35 \mathrm{~m} \end{aligned} $$ which is the length of the rope.

Hence, the correct answer is option: 'D'.

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