Sure! Let's work through each part of this problem step-by-step.
### Part A: Finding the Perimeter of the Circular Field
The perimeter of a circular field is also known as the circumference. The formula to calculate the circumference [tex]\( C \)[/tex] of a circle is:
[tex]\[ C = 2 \pi r \][/tex]
where:
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159 (but it’s given as [tex]\(\frac{22}{7}\)[/tex] for this problem),
- [tex]\( r \)[/tex] is the radius of the circle.
Given:
- The radius [tex]\( r \)[/tex] is 63 meters,
- [tex]\(\pi = \frac{22}{7}\)[/tex].
Now, substitute the given values into the formula:
[tex]\[ C = 2 \cdot \left(\frac{22}{7}\right) \cdot 63 \][/tex]
When you do the calculation,
[tex]\[ C = 2 \cdot \frac{22}{7} \cdot 63 = 396 \][/tex]
So, the perimeter (circumference) of the field is 396 meters.
### Part B: Finding the Length of Wire Required for 5 Rounds
To fence the field with 5 rounds, we need to calculate the total length of wire needed. This is essentially 5 times the perimeter of the field.
We already found the circumference (perimeter) to be 396 meters.
To find the total length of wire for 5 rounds:
[tex]\[ \text{Total wire length} = 5 \times \text{Perimeter} \][/tex]
[tex]\[ \text{Total wire length} = 5 \times 396 \][/tex]
This gives:
[tex]\[ \text{Total wire length} = 1980 \][/tex]
Therefore, the length of wire required to fence the field with 5 rounds is 1980 meters.
