A circular field of radius 105 m has a circular path of uniform width of 5 m along and inside its boundary. Find the area of the path.

Answer

To find the area of the circular path inside the circular field, we can follow these steps:

### Step 1: Identify the radii
- The radius of the outer circular field (C1) is given as \( r_1 = 105 \) m.
- The width of the path is \( 5 \) m, so the radius of the inner circle (C2) is:
\[ r_2 = r_1 - 5 = 105 - 5 = 100 \text{ m} \]

### Step 2: Calculate the area of the outer circle (C1)
- The area of a circle is calculated using the formula:
\[ \text{Area} = \pi r^2 \]
- Therefore, the area of the outer circle (C1) is:
\[ \text{Area of C1} = \pi r_1^2 = \pi (105)^2 = \pi \times 11025 \]

### Step 3: Calculate the area of the inner circle (C2)
- Similarly, the area of the inner circle (C2) is:
\[ \text{Area of C2} = \pi r_2^2 = \pi (100)^2 = \pi \times 10000 \]

### Step 4: Find the area of the path
- The area of the path is the difference between the area of the outer circle and the area of the inner circle:
\[ \text{Area of the path} = \text{Area of C1} - \text{Area of C2} \]
- Substituting the areas we calculated:
\[ \text{Area of the path} = \pi (11025 - 10000) = \pi \times 1025 \]

### Step 5: Substitute the value of \(\pi\)
- Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of the path} = \frac{22}{7} \times 1025 \]

### Step 6: Calculate the area
- Now, calculate the area:
\[ \text{Area of the path} = \frac{22 \times 1025}{7} \]
\[ = \frac{22550}{7} \approx 3214.2857 \text{ m}^2 \]
- Rounding to one decimal place, we get:
\[ \text{Area of the path} \approx 3214.3 \text{ m}^2 \]

### Final Answer
The area of the path is approximately **3214.3 m²**.

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