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)

Question

Responses

A=112.5π ft.2
upper A equals 112.5 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=56.25π ft.2

Answer 1

To find the area that the sprinkler can spray, we first need to understand that the sprinkler creates a sector of a circle when it rotates 180°.

1. Radius of the sector: The radius is the distance that the sprinkler can shoot water, which is 15 feet.

2. Angle of the sector: The angle is 180°.

The formula for the area of a sector of a circle is given by:

\[ A = \frac{\theta}{360°} \times \pi r^2 \]

Where:

• \(A\) is the area of the sector,
• \(\theta\) is the angle in degrees,
• \(r\) is the radius.

Plugging in the values for this problem:

• \(r = 15\) feet
• \(\theta = 180°\)

Now, calculate the area:

\[ A = \frac{180°}{360°} \times \pi (15)^2 \] \[ A = \frac{1}{2} \times \pi \times 225 \] \[ A = \frac{225\pi}{2} \] \[ A = 112.5\pi , \text{ft}^2 \]

Therefore, the area that the sprinkler can spray is:

\[ A = 112.5\pi , \text{ft}^2 \]

The correct response is:

A=112.5π ft².