There is a rectangular plot, 120m long and 98m wide, with semi-circular flower beds along the breath on both sides of the plot. The cost of putting a fence all around the plot at ₹16.50 per m is: (Taken `pi=22/7`)

Options

A. ₹8,910
B. ₹9,042
C. ₹9,009
D. ₹8,943

Answer

To find the cost of putting a fence all around the rectangular plot with semi-circular flower beds, we need to follow these steps:

### Step 1: Understand the dimensions of the plot
The rectangular plot has the following dimensions:
- Length (L) = 120 m
- Width (W) = 98 m

### Step 2: Calculate the radius of the semi-circles
The semi-circular flower beds are along the width of the plot. The diameter of each semi-circle is equal to the width of the plot.
- Diameter of semi-circle = Width = 98 m
- Radius (r) = Diameter / 2 = 98 m / 2 = 49 m

### Step 3: Calculate the perimeter of the plot
The total perimeter consists of the lengths of the rectangle plus the curved parts of the two semi-circles.

1. The length of the two longer sides (lengths) = 2 * Length = 2 * 120 m = 240 m
2. The circumference of one full circle with radius 49 m is given by the formula:
\[ \text{Circumference} = 2 \pi r = 2 \times \frac{22}{7} \times 49 \]
So, the circumference of one full circle is:
\[ = 2 \times \frac{22}{7} \times 49 = \frac{22 \times 98}{7} = \frac{2156}{7} \approx 308 m \]
Since we have two semi-circles, the total length contributed by the semi-circles is equal to the circumference of one full circle:
\[ \text{Total length of semi-circles} = 308 m \]

3. Therefore, the total perimeter (P) of the plot is:
\[ P = \text{Length of two sides} + \text{Length of two semi-circles} = 240 m + 308 m = 548 m \]

### Step 4: Calculate the cost of fencing
The cost of putting a fence is given at ₹16.50 per meter. Thus, the total cost (C) can be calculated as:
\[ C = \text{Perimeter} \times \text{Cost per meter} = 548 m \times 16.50 \]
Calculating this gives:
\[ C = 548 \times 16.50 = 9042 \]

### Final Answer
The cost of putting a fence all around the plot is ₹9042.

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