Sure, let's solve the problem step-by-step.
### Step 1: Calculate the Perimeter of the Circular Field
The formula to find the perimeter (circumference) of a circle is given by:
[tex]\[ \text{Perimeter} = 2 \pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
Given:
Radius ([tex]\( r \)[/tex]) = 63 meters
By substituting the radius into the formula:
[tex]\[ \text{Perimeter} = 2 \pi \times 63 \][/tex]
[tex]\[ \text{Perimeter} = 395.84067435231395 \text{ meters} \][/tex]
So, the perimeter of the circular field is approximately 395.84 meters.
### Step 2: Calculate the Total Length of Wire Required for 5 Rounds
Since we need to fence the field with 5 rounds of wire, we multiply the perimeter by 5:
[tex]\[ \text{Total Wire Length} = \text{Perimeter} \times 5 \][/tex]
[tex]\[ \text{Total Wire Length} = 395.84067435231395 \times 5 \][/tex]
[tex]\[ \text{Total Wire Length} = 1979.2033717615698 \text{ meters} \][/tex]
So, the total length of wire required for 5 rounds is approximately 1979.20 meters.
### Step 3: Calculate the Total Cost of Fencing
The cost of fencing is given as Rs 50 per meter. To find the total cost, we multiply the total length of the wire needed by the cost per meter:
[tex]\[ \text{Total Cost} = \text{Total Wire Length} \times \text{Cost per meter} \][/tex]
[tex]\[ \text{Total Cost} = 1979.2033717615698 \times 50 \][/tex]
[tex]\[ \text{Total Cost} = 98960.1685880785 \text{ Rs} \][/tex]
So, the total cost of fencing the circular field with 5 rounds of wire is approximately Rs 98960.17.
