In a rectangular plot of land 70 m long and 40 m board , a circular garden of radius 17.5 m is developed . Find the cost of turfing the remaining portion at the rate of Rs. 28.50 per sq . Metre .

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Area of the Rectangular Plot
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 70 m
- Breadth = 40 m

Calculating the area:
\[ \text{Area of the plot} = 70 \, \text{m} \times 40 \, \text{m} = 2800 \, \text{m}^2 \]

### Step 2: Calculate the Area of the Circular Garden
The area of a circle is given by the formula:
\[ \text{Area} = \pi r^2 \]
Given:
- Radius \( r = 17.5 \, \text{m} \)
- Using \( \pi \approx \frac{22}{7} \) or \( 3.14 \)

Calculating the area:
\[ \text{Area of the garden} = \pi \times (17.5 \, \text{m})^2 \]
Calculating \( (17.5)^2 \):
\[ (17.5)^2 = 306.25 \]
Now substituting back:
\[ \text{Area of the garden} = \frac{22}{7} \times 306.25 \approx 962.5 \, \text{m}^2 \]

### Step 3: Calculate the Area of the Remaining Portion
The area of the remaining portion is found by subtracting the area of the circular garden from the area of the rectangular plot:
\[ \text{Area of remaining portion} = \text{Area of plot} - \text{Area of garden} \]
Substituting the values:
\[ \text{Area of remaining portion} = 2800 \, \text{m}^2 - 962.5 \, \text{m}^2 = 1837.5 \, \text{m}^2 \]

### Step 4: Calculate the Cost of Turfing
The cost of turfing is calculated by multiplying the area of the remaining portion by the cost per square meter:
\[ \text{Cost of turfing} = \text{Area of remaining portion} \times \text{Cost per sq. m} \]
Given:
- Cost per sq. m = Rs. 28.50

Calculating the cost:
\[ \text{Cost of turfing} = 1837.5 \, \text{m}^2 \times 28.50 \, \text{Rs/m}^2 = 52,368.75 \, \text{Rs} \]

### Final Answer
The cost of turfing the remaining portion is Rs. 52,368.75.

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