To find the area of the lawn that receives water from the sprinkler, we need to consider the sector formed by the sprinkler’s spray. The formula for the area of a sector is:
Area = (θ/360) × π × r²
where θ is the angle in degrees, and r is the radius (distance the water sprays).
In this case, the radius (r) is 24 feet, and the angle (θ) is 150 degrees.
Plugging in these values:
Area = (150/360) × π × (24)²
Calculating this step by step:
1. First, we calculate (24)² = 576.
2. Then, substituting back into the formula:
Area = (150/360) × π × 576
3. Simplifying (150/360) gives us 5/12.
Therefore, Area = (5/12) × π × 576.
4. Now, multiplying this out, we get: Area ≈ (5/12) × 3.14 × 576 = (5 × 3.14 × 576) / 12.
5. This approximates to Area ≈ 754.67 square feet.
Thus, the area of the lawn that receives water from the sprinkler is approximately 754.67 square feet.