A cow is tied on the corner of a rectangular field of size `30m xx 20 m` by a 14m long rope. The area of the region, that she can graze is (use `pi = (22)/(7)`) :

Options

A. `350 m^(2)`
B. `196 m^(2)`
C. `154 m^(2)`
D. `22m^(2)`

Answer

To find the area of the region that the cow can graze, we need to consider the circular sector that the cow can access due to the length of the rope. The cow is tied at a corner of a rectangular field, which means it can graze in a quarter-circle area.

### Step-by-Step Solution:

1. **Identify the parameters:**
- Length of the rope (radius, r) = 14 m
- Since the cow is tied at a corner, it can graze in a quarter-circle.

2. **Calculate the area of the quarter-circle:**
- The formula for the area of a circle is given by:
\[ \text{Area} = \pi r^2 \]
- For a quarter-circle, the area will be:
\[ \text{Area of quarter-circle} = \frac{1}{4} \pi r^2 \]

3. **Substituting the values:**
- We know \( r = 14 \) m and we will use \( \pi = \frac{22}{7} \).
- First, calculate \( r^2 \):
\[ r^2 = 14^2 = 196 \]
- Now substitute \( r^2 \) into the area formula:
\[ \text{Area} = \frac{1}{4} \times \frac{22}{7} \times 196 \]

4. **Simplifying the expression:**
- Calculate \( \frac{22 \times 196}{7} \):
\[ \frac{22 \times 196}{7} = \frac{4312}{7} = 616 \]
- Now divide by 4:
\[ \text{Area} = \frac{616}{4} = 154 \text{ m}^2 \]

5. **Final Result:**
- The area of the region that the cow can graze is \( 154 \text{ m}^2 \).