Question

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=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**.