A circular pond is 17.5 m of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per `m^2`?

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the radius of the circular pond
The diameter of the pond is given as 17.5 m. To find the radius, we use the formula:
\[ \text{Radius} = \frac{\text{Diameter}}{2} \]
So,
\[ \text{Radius of the pond} = \frac{17.5}{2} = 8.75 \text{ m} \]

### Step 2: Calculate the radius of the outer circle (pond + path)
The path surrounding the pond is 2 m wide. Therefore, the radius of the outer circle (which includes the pond and the path) is:
\[ \text{Outer radius} = \text{Radius of the pond} + \text{Width of the path} \]
So,
\[ \text{Outer radius} = 8.75 + 2 = 10.75 \text{ m} \]

### Step 3: Calculate the area of the outer circle
The area of a circle is given by the formula:
\[ \text{Area} = \pi r^2 \]
Using the outer radius:
\[ \text{Area of the outer circle} = \pi (10.75)^2 \]
Calculating this:
\[ \text{Area of the outer circle} = \pi \times 115.5625 \approx 363.24 \text{ m}^2 \quad (\text{using } \pi \approx 3.14) \]

### Step 4: Calculate the area of the inner circle (pond)
Now, we calculate the area of the pond using its radius:
\[ \text{Area of the inner circle} = \pi (8.75)^2 \]
Calculating this:
\[ \text{Area of the inner circle} = \pi \times 76.5625 \approx 240.83 \text{ m}^2 \]

### 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 area of the inner circle:
\[ \text{Area of the path} = \text{Area of the outer circle} - \text{Area of the inner circle} \]
So,
\[ \text{Area of the path} = 363.24 - 240.83 \approx 122.41 \text{ m}^2 \]

### Step 6: Calculate the cost of constructing the path
The cost of constructing the path is given by the area of the path multiplied by the cost per square meter:
\[ \text{Cost} = \text{Area of the path} \times \text{Cost per m}^2 \]
Substituting the values:
\[ \text{Cost} = 122.41 \times 25 \approx 3060.25 \]

### Final Answer
The cost of constructing the path is approximately Rs. 3060.25.

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