A circular running track has inner radius 126 m and outer radius 140 m . Find the area of the track .

Answer

To find the area of the circular running track, we need to calculate the area of the outer circle and subtract the area of the inner circle. Here’s a step-by-step solution:

### Step 1: Identify the inner and outer radii
- Inner radius (R_i) = 126 m
- Outer radius (R_o) = 140 m

### Step 2: Calculate the area of the outer circle
The formula for the area of a circle is given by:
\[ A = \pi R^2 \]
For the outer circle:
\[ A_o = \pi R_o^2 \]
Substituting the value of R_o:
\[ A_o = \pi (140)^2 \]
Calculating \( (140)^2 \):
\[ (140)^2 = 19600 \]
Now substituting this back into the area formula:
\[ A_o = \pi \times 19600 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A_o = \frac{22}{7} \times 19600 \]
Calculating:
\[ A_o = \frac{22 \times 19600}{7} = \frac{431200}{7} \approx 61743 \text{ m}^2 \]

### Step 3: Calculate the area of the inner circle
Using the same formula for the inner circle:
\[ A_i = \pi R_i^2 \]
Substituting the value of R_i:
\[ A_i = \pi (126)^2 \]
Calculating \( (126)^2 \):
\[ (126)^2 = 15876 \]
Now substituting this back into the area formula:
\[ A_i = \pi \times 15876 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A_i = \frac{22}{7} \times 15876 \]
Calculating:
\[ A_i = \frac{22 \times 15876}{7} = \frac{349272}{7} \approx 49910 \text{ m}^2 \]

### Step 4: Find the area of the track
The area of the track is the difference between the area of the outer circle and the area of the inner circle:
\[ \text{Area of the track} = A_o - A_i \]
Substituting the values we calculated:
\[ \text{Area of the track} = 61743 - 49910 \]
Calculating:
\[ \text{Area of the track} = 11833 \text{ m}^2 \]

### Final Answer:
The area of the circular running track is approximately **11833 m²**.

---