To determine the area of the lawn that the water from the sprinkler would cover, we need to calculate the area of the sector that the sprinkler covers. The formula for the area of a sector of a circle is:
Area = (θ/360) × πr²
Where:
- θ is the angle of the sector in degrees.
- r is the radius of the circle.
- π is a constant (approximately 3.14159).
Given:
- θ = 120 degrees
- r = 40 feet
Plugging these values into the formula:
Area = (120/360) × π × (40)²
First, calculate the fraction of the circle:
120/360 = 1/3
Next, calculate the square of the radius:
(40)² = 1600
Now, multiply these values together:
Area = (1/3) × π × 1600
Finally, multiply by π:
Area ≈ (1/3) × 3.14159 × 1600
Area ≈ 1675.52 square feet
Therefore, the area of the lawn that the water from the sprinkler would cover is approximately 1675.52 square feet.