Find the length of a rope by which a cow must be tethered in order that it may be ble to graze an area of 154 sq m

Options

A. 7 m
B. 8 m
C. 12 m
D. 13 m

Answer

To find the length of the rope by which a cow must be tethered in order to graze an area of 154 square meters, we can follow these steps:

### Step 1: Understand the Area of a Circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Set Up the Equation
We know from the problem that the area \( A \) is 154 square meters. Therefore, we can set up the equation:
\[ \pi r^2 = 154 \]

### Step 3: Solve for \( r^2 \)
To isolate \( r^2 \), we need to divide both sides of the equation by \( \pi \):
\[ r^2 = \frac{154}{\pi} \]

### Step 4: Substitute the Value of \( \pi \)
Using the approximation \( \pi \approx \frac{22}{7} \), we can substitute this value into the equation:
\[ r^2 = \frac{154}{\frac{22}{7}} = 154 \times \frac{7}{22} \]

### Step 5: Simplify the Calculation
Now, we can simplify the right side:
\[ r^2 = \frac{154 \times 7}{22} \]
Calculating \( 154 \div 22 \):
\[ 154 \div 22 = 7 \]
Thus, we have:
\[ r^2 = 7 \times 7 = 49 \]

### Step 6: Find \( r \)
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{49} = 7 \]

### Conclusion
The length of the rope by which the cow must be tethered is:
\[ \text{Length of the rope} = 7 \text{ meters} \]

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