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=7.5π ft.2
upper A equals 7.5 pi ft. squared

A=56.25π ft.2
upper A equals 56.25 pi ft. squared

A=112.5π ft.2
upper A equals 112.5 pi ft. squared

A=225π ft.2

Answer 1

To find the area that the sprinkler can spray, we'll start by determining the area of the semicircle that represents the area covered by the sprinkler as it rotates 180°.

The formula for the area of a circle is:

\[ A = \pi r^2 \]

Since the sprinkler only covers a semicircle (180°), we will take half of the area of the full circle. The radius \( r \) in this case is the distance from the sprinkler head, which is 15 feet.

First, calculate the area of the full circle:

\[ A_{\text{circle}} = \pi (15)^2 = \pi (225) = 225\pi \text{ ft}^2 \]

Now, to find the area of the semicircle:

\[ A_{\text{semicircle}} = \frac{1}{2} A_{\text{circle}} = \frac{1}{2} (225\pi) = 112.5\pi \text{ ft}^2 \]

Thus, the area of the backyard that the sprinkler can spray is:

\[ \boxed{112.5\pi \text{ ft}^2} \]