To find the circumference of the area being watered by the irrigation sprinkler, follow these steps:
1. Understand the Problem:
The radius of the sprinkler's spray is given as \(12.6 \, \text{m}\).
We need to determine the circumference of the circle formed by this spray.
2. Recall the Formula:
The circumference \(C\) of a circle can be calculated using the formula:
[tex]\[
C = 2\pi r
\][/tex]
where \(r\) is the radius of the circle and \(\pi\) (pi) is a mathematical constant approximately equal to \(3.14159\).
3. Substitute the Given Radius into the Formula:
Here, the radius \(r\) is \(12.6 \, \text{m}\). Substituting \(r = 12.6\) into the circumference formula:
[tex]\[
C = 2 \pi \times 12.6
\][/tex]
4. Perform the Calculation:
Next, we perform the multiplication:
[tex]\[
C = 2 \times 3.14159 \times 12.6 \approx 79.16813487046278 \, \text{m}
\][/tex]
Therefore, the circumference of the area being watered by the sprinkler is approximately [tex]\(79.168 \, \text{m}\)[/tex].
