To solve the problem step by step, we will calculate the area of the park, the area of the uncobbled part, the area of the cobblestoned part, and finally the total cost of laying the cobblestones.
### Step 1: Calculate the area of the park
The park is rectangular, so we can find its area using the formula:
\[
\text{Area of the park} = \text{Length} \times \text{Width}
\]
Given:
- Length = 76 m
- Width = 58 m
Calculating:
\[
\text{Area of the park} = 76 \, \text{m} \times 58 \, \text{m} = 4408 \, \text{m}^2
\]
### Step 2: Calculate the dimensions of the uncobbled area
The cobblestone path is 8 m wide, which means we need to subtract 8 m from each side of the length and width of the park to find the dimensions of the uncobbled area.
New length:
\[
\text{New Length} = 76 \, \text{m} - 2 \times 8 \, \text{m} = 76 \, \text{m} - 16 \, \text{m} = 60 \, \text{m}
\]
New width:
\[
\text{New Width} = 58 \, \text{m} - 2 \times 8 \, \text{m} = 58 \, \text{m} - 16 \, \text{m} = 42 \, \text{m}
\]
### Step 3: Calculate the area of the uncobbled part
Now we can calculate the area of the uncobbled part using the new dimensions:
\[
\text{Area of uncobbled part} = \text{New Length} \times \text{New Width}
\]
Calculating:
\[
\text{Area of uncobbled part} = 60 \, \text{m} \times 42 \, \text{m} = 2520 \, \text{m}^2
\]
### Step 4: Calculate the area of the cobblestoned part
To find the area of the cobblestoned part, we subtract the area of the uncobbled part from the area of the park:
\[
\text{Area of cobblestoned part} = \text{Area of park} - \text{Area of uncobbled part}
\]
Calculating:
\[
\text{Area of cobblestoned part} = 4408 \, \text{m}^2 - 2520 \, \text{m}^2 = 1888 \, \text{m}^2
\]
### Step 5: Calculate the total cost of the job
The cost of laying cobblestones is ₹ 35 per square meter. Therefore, we can calculate the total cost:
\[
\text{Total cost} = \text{Area of cobblestoned part} \times \text{Cost per square meter}
\]
Calculating:
\[
\text{Total cost} = 1888 \, \text{m}^2 \times 35 \, \text{₹/m}^2 = 66,080 \, \text{₹}
\]
### Final Answer
The total cost of laying the cobblestones is **₹ 66,080**.
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