The circumference of a circular playground 1s 308 metre. There is 7 metre wide path around the ground. The area of the path is

Options

A. 2130 sq. metre
B. 2410 sq. metre
C. 2510 sq. metre
D. 2310 sq. metre

Explanation

To find the area of the path around the circular playground, we can follow these steps:

### Step 1: Find the radius of the playground
The circumference of the circular playground is given as 308 meters. The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
Where \( r \) is the radius of the circle. We can rearrange this formula to find the radius:
\[ r = \frac{C}{2\pi} \]

Substituting the given circumference:
\[ r_1 = \frac{308}{2 \times \frac{22}{7}} \]
\[ r_1 = \frac{308 \times 7}{44} \]
\[ r_1 = \frac{2156}{44} \]
\[ r_1 = 49 \text{ meters} \]

### Step 2: Find the radius of the outer circle
The path around the playground is 7 meters wide. Therefore, the radius of the outer circle (r2) is:
\[ r_2 = r_1 + 7 \]
\[ r_2 = 49 + 7 = 56 \text{ meters} \]

### Step 3: Calculate the area of the outer circle
The area (A) of a circle is given by the formula:
\[ A = \pi r^2 \]
For the outer circle:
\[ A_{outer} = \pi r_2^2 = \pi (56^2) \]
\[ A_{outer} = \frac{22}{7} \times 56^2 \]
\[ A_{outer} = \frac{22}{7} \times 3136 \]
\[ A_{outer} = \frac{22 \times 3136}{7} \]
\[ A_{outer} = \frac{69092}{7} \]
\[ A_{outer} = 9870.2857 \text{ square meters} \] (approximately)

### Step 4: Calculate the area of the inner circle
For the inner circle:
\[ A_{inner} = \pi r_1^2 = \pi (49^2) \]
\[ A_{inner} = \frac{22}{7} \times 49^2 \]
\[ A_{inner} = \frac{22}{7} \times 2401 \]
\[ A_{inner} = \frac{22 \times 2401}{7} \]
\[ A_{inner} = \frac{52822}{7} \]
\[ A_{inner} = 7546.2857 \text{ square meters} \] (approximately)

### Step 5: Calculate the area of the path
The area of the path is the difference between the area of the outer circle and the inner circle:
\[ A_{path} = A_{outer} - A_{inner} \]
\[ A_{path} = 9870.2857 - 7546.2857 \]
\[ A_{path} = 2324 \text{ square meters} \] (approximately)

### Final Answer
The area of the path is approximately **2324 square meters**.

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