If a rotating water sprinkler is a set tto 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

To calculate the area of the lawn that the water from the sprinkler would cover, we need to find the sector of the circle that corresponds to the 120-degree rotation and subtract the remaining area of the circle.

1. First, let's find the area of the sector:
- The radius of the sprinkler is given as 40 feet.
- The measure of the angle is 120 degrees.
- The formula to calculate the area of a sector is: A = (θ/360) * π * r^2, where A is the area, θ is the angle in degrees, π is a constant (approximately 3.14), and r is the radius.
- Plugging in the values, we get: A_sector = (120/360) * π * (40^2)

2. Next, we need to find the area of the remaining circle:
- The formula to calculate the area of a circle is: A_circle = π * r^2.
- Since we already have the radius (40 feet), we can directly substitute it into the formula to get: A_circle = π * (40^2)

3. Finally, we can calculate the area of the lawn that the sprinkler covers by subtracting the area of the remaining circle from the area of the sector: A_lawn = A_sector - A_circle.

Computing the values of A_sector and A_circle using a calculator or computer program, such as Python or Excel, will give you the answer for A_lawn.

120/360 = 1/3

so
(1/3) pi r^2
or
(1/3)(3.14)(40)(40)