A cow is tied in a pole with a rope. The cow moves in a circular pan keeping rope straight. When it covers a distance of 44 meter an angle of 72° is subtended at the centre. The length of the rope is:

Options

A. 45 m
B. 35 m
C. 22 m
D. 56 m

Answer

To find the length of the rope, we can use the relationship between the arc length, the radius of the circular path, and the angle subtended at the center. The formula for the arc length \( L \) is given by:

\[ L = \frac{\theta}{360^\circ} \times 2\pi r \]

Where:
- \( L \) is the arc length,
- \( \theta \) is the angle in degrees,
- \( r \) is the radius (length of the rope).

Given:
- \( L = 44 \) meters,
- \( \theta = 72^\circ \).

We need to find the radius \( r \).

### Step 1: Substitute the known values into the formula

\[ 44 = \frac{72}{360} \times 2\pi r \]

### Step 2: Simplify the fraction

\[ \frac{72}{360} = \frac{1}{5} \quad \text{(since } 72 \div 72 = 1 \text{ and } 360 \div 72 = 5\text{)} \]

Now the equation becomes:

\[ 44 = \frac{1}{5} \times 2\pi r \]

### Step 3: Multiply both sides by 5 to eliminate the fraction

\[ 44 \times 5 = 2\pi r \]

\[ 220 = 2\pi r \]

### Step 4: Divide both sides by \( 2\pi \)

\[ r = \frac{220}{2\pi} \]

### Step 5: Substitute \( \pi \) with \( \frac{22}{7} \)

\[ r = \frac{220}{2 \times \frac{22}{7}} = \frac{220 \times 7}{44} \]

### Step 6: Simplify the expression

\[ r = \frac{1540}{44} = 35 \text{ meters} \]

Thus, the length of the rope is **35 meters**.

### Final Answer:
The length of the rope is **35 meters**.

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