To find the maximum area that can be irrigated by the sprinkler, we can first visualize the area it covers as a sector of a circle.
The formula for the area of a sector is:
A = (θ / 360) * π * r²
Where:
- A = area of the sector
- θ = angle in degrees
- r = radius (distance the sprinkler can spray)
In this case, the radius (r) is 40 meters, and the angle (θ) is 120 degrees. Plugging the numbers into the formula gives:
A = (120 / 360) * π * (40)²
A = (1/3) * π * 1600
A = (1600π) / 3
Calculating that, we have:
A ≈ 1675.52 square meters (using π ≈ 3.14)
Thus, the maximum area that can be irrigated by the sprinkler system is approximately 1675.52 square meters.