A cow is tied to a pole fixed at one corner of a square field of grass , whose side is 40 m . If the length of the rope with which the cow is tied is 14 m , then what is the area in which the cow can graze ?

Answer

To find the area in which the cow can graze, we need to consider the following steps:

### Step 1: Understand the setup
The cow is tied to a pole at one corner of a square field. The side of the square field is 40 meters, and the length of the rope is 14 meters.

### Step 2: Visualize the grazing area
Since the cow is tied at one corner, it can graze in a quarter-circle area with a radius equal to the length of the rope (14 m).

### Step 3: Calculate the area of the quarter-circle
The formula for the area of a circle is given by:
\[ \text{Area of circle} = \pi r^2 \]
Since we only need the area of a quarter-circle, we will use:
\[ \text{Area of quarter-circle} = \frac{1}{4} \pi r^2 \]
Substituting \( r = 14 \) m:
\[ \text{Area of quarter-circle} = \frac{1}{4} \pi (14)^2 \]

### Step 4: Calculate \( (14)^2 \)
\[ (14)^2 = 196 \]

### Step 5: Substitute back into the area formula
\[ \text{Area of quarter-circle} = \frac{1}{4} \pi \times 196 \]

### Step 6: Calculate the area
Using \( \pi \approx 3.14 \):
\[ \text{Area of quarter-circle} = \frac{1}{4} \times 3.14 \times 196 \]
\[ = \frac{1}{4} \times 615.44 \]
\[ = 153.86 \text{ m}^2 \]

### Final Answer
The area in which the cow can graze is approximately \( 153.86 \text{ m}^2 \).

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