To find the cost of constructing the path, we need to calculate the area of the path surrounding the park.

Step 1: Find the Radius of the Park and the Path

• Radius of the park = Diameter / 2 = 17.5 m / 2 = 8.75 m
• The width of the path around the park is 2 m, so the total radius (park + path) = 8.75 m + 2 m = 10.75 m

Step 2: Calculate the Area of the Larger Circle (Park + Path)

$\text{Area of larger circle} = \pi \times (\text{Total radius})^2 = \frac{22}{7} \times (10.75)^2$ $= \frac{22}{7} \times 115.5625 = 363.25 \, \text{m}^2$

Step 3: Calculate the Area of the Park (Inner Circle)

$\text{Area of park} = \pi \times (\text{Radius of park})^2 = \frac{22}{7} \times (8.75)^2$ $= \frac{22}{7} \times 76.5625 = 240.25 \, \text{m}^2$

Step 4: Calculate the Area of the Path

$\text{Area of path} = \text{Area of larger circle} - \text{Area of park}$ $= 363.25 - 240.25 = 123 \, \text{m}^2$

Step 5: Calculate the Cost of Constructing the Path

$\text{Cost} = \text{Area of path} \times \text{Rate per square metre}$ $= 123 \times 25 = ₹3075$

Answer

The cost of constructing the path is ₹3075.

Would you like to go over any steps in more detail, or have further questions?

1. How would the cost change if the path were wider?
2. What if the rate per square meter was different?
3. How would the solution change if the park were rectangular?
4. Can this method apply to other shapes like an elliptical path?
5. What if the park had additional structures taking up space?

Tip: When calculating areas involving circular shapes, always start by identifying inner and outer radii.