If a rotating water sprinkler is set so spray water out at a radius of 40 feet around a circular revolution of 120 degrees, what is the area of the lawn that the water from the sprinkler would then cover? Round to the nearest tenth
533.3ft?
Oops didn't mean to ask this again
To find the area covered by the water from the sprinkler, we need to calculate the area of a circular sector.
1. First, let's find the central angle of the circular sector covered by the sprinkler's spray. The given angle is 120 degrees, which is already in degrees.
2. Next, we need to convert this angle to radians since the formula for the area of a circular sector uses radians. To convert degrees to radians, we use the conversion factor: 1 radian = (π/180) degrees.
Central angle in radians = (120 degrees) × (π/180) ≈ 2.0944 radians
3. The radius of the spray is given as 40 feet.
4. Now, we can calculate the area of the circular sector. The formula is:
Area of sector = (1/2) × r^2 × theta
where r is the radius and theta is the central angle.
Area of the sector = (1/2) × (40 feet)^2 × 2.0944 radians ≈ 3351.8 square feet
So, the area of the lawn covered by the water from the sprinkler is approximately 3351.8 square feet when rounded to the nearest tenth.
To find the area of the lawn covered by the water sprinkler, we need to calculate the area of the sector formed by the rotating water spray.
The formula to find the area of a sector is given by:
Area = (θ/360) * π * r^2
Where:
θ is the angle in degrees (in this case, 120 degrees)
π is a constant approximately equal to 3.14159
r is the radius of the circle (in this case, 40 feet)
Let's calculate the area:
Area = (120/360) * 3.14159 * (40^2)
Area = (1/3) * 3.14159 * 1600
Area = 1.0472 * 1600
Area ≈ 1675.52 square feet
Rounding to the nearest tenth, the area covered by the water sprinkler is approximately 1675.5 square feet.
Therefore, the answer of 533.3ft seems to be incorrect.