What would be the cost of building a 7 metres wide garden around a circular field with diameter equal to 280 metres. If the cost per sq. metre for building the garden is Rs. 21?

Options

A. Rs 1,56,242
B. Rs. 2,48,521
C. Rs. 1,11,624
D. None of these

Answer

To solve the problem of finding the cost of building a 7 meters wide garden around a circular field with a diameter of 280 meters, we can follow these steps:

### Step 1: Calculate the radius of the circular field.
The radius \( r \) of the circular field can be calculated by dividing the diameter by 2.
\[ r = \frac{280 \text{ m}}{2} = 140 \text{ m} \]

### Step 2: Calculate the radius of the garden including the width.
The garden is 7 meters wide, so we need to add this width to the radius of the circular field.
\[ \text{Radius of the garden} = r + 7 \text{ m} = 140 \text{ m} + 7 \text{ m} = 147 \text{ m} \]

### Step 3: Calculate the area of the circular field.
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
First, we calculate the area of the circular field:
\[ A_{\text{field}} = \pi (140 \text{ m})^2 = \pi \times 19600 \text{ m}^2 \approx 61575.4 \text{ m}^2 \]

### Step 4: Calculate the area of the garden including the circular field.
Now, we calculate the area of the larger circle that includes the garden:
\[ A_{\text{garden}} = \pi (147 \text{ m})^2 = \pi \times 21609 \text{ m}^2 \approx 67857.6 \text{ m}^2 \]

### Step 5: Calculate the area of the garden alone.
To find the area of the garden itself, we subtract the area of the circular field from the area of the larger circle:
\[ A_{\text{garden only}} = A_{\text{garden}} - A_{\text{field}} = 67857.6 \text{ m}^2 - 61575.4 \text{ m}^2 \approx 6272.2 \text{ m}^2 \]

### Step 6: Calculate the cost of building the garden.
The cost of building the garden can be calculated by multiplying the area of the garden by the cost per square meter:
\[ \text{Cost} = A_{\text{garden only}} \times \text{Cost per sq. meter} = 6272.2 \text{ m}^2 \times 21 \text{ Rs/m}^2 \approx 131,707.2 \text{ Rs} \]

### Final Answer:
The cost of building the garden around the circular field is approximately **Rs. 131,707.2**.

---