The length of a rope by which a buffalo must be tethered so that she may be able to graze a grassy area of 2464 sq. m is :

Options

A. 35 m
B. 27 m
C. 24 m
D. 28 m

Answer

To find the length of the rope by which a buffalo must be tethered to graze an area of 2464 sq. m, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: The buffalo grazes in a circular area when tethered. The area of this circle is given as 2464 sq. m.

2. **Use the Formula for the Area of a Circle**: The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

3. **Set Up the Equation**: We know the area \( A \) is 2464 sq. m, so we can set up the equation:
\[ \pi r^2 = 2464 \]

4. **Substitute the Value of \( \pi \)**: For our calculations, we can use \( \pi \approx \frac{22}{7} \). Thus, the equation becomes:
\[ \frac{22}{7} r^2 = 2464 \]

5. **Clear the Fraction**: Multiply both sides by 7 to eliminate the fraction:
\[ 22 r^2 = 2464 \times 7 \]

6. **Calculate \( 2464 \times 7 \)**:
\[ 2464 \times 7 = 17248 \]
So, we have:
\[ 22 r^2 = 17248 \]

7. **Solve for \( r^2 \)**: Divide both sides by 22:
\[ r^2 = \frac{17248}{22} \]

8. **Calculate \( \frac{17248}{22} \)**:
\[ r^2 = 784 \]

9. **Find \( r \)**: Take the square root of both sides to find \( r \):
\[ r = \sqrt{784} = 28 \]

10. **Conclusion**: The length of the rope by which the buffalo must be tethered is:
\[ \text{Length of the rope} = 28 \text{ meters} \]

### Final Answer:
The length of the rope is **28 meters**.