There is a sprinkler in Amut’s backyard that can shoot water a distance of 15 feet from the sprinkler head. It rotates on the center point at an angle of 180° before returning to its starting position. What area of the backyard, in feet, can the sprinkler spray?(1 point)
Responses
A=56.25π ft.2
upper A equals 56.25 pi ft. squared
A=7.5π ft.2
upper A equals 7.5 pi ft. squared
A=225π ft.2
upper A equals 225 pi ft. squared
A=112.5π ft.2
To find the area that the sprinkler can spray, we need to find the area of the sector created by the 180° angle.
First, find the radius of the circle. Since the distance from the sprinkler head is 15 feet, the radius is 15 feet.
The formula to find the area of a sector is given by A = (θ/360°) * π * r², where θ is the angle and r is the radius.
Plugging in the values, we get A = (180°/360°) * π * (15 ft)² = 0.5 * π * 225 ft² = 112.5π ft².
Therefore, the area of the backyard that the sprinkler can spray is A = 112.5π ft².
So the correct answer is: A=112.5π ft.2.