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=225π ft.2
upper A equals 225 pi ft. squared

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

A=56.25π ft.2

Answer 1

To find the area that the sprinkler can spray, we first note that it sprays in a semicircular area because it rotates 180°. The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius.

Given:

• The distance the sprinkler can spray (radius) \( r = 15 \) feet.
• The area for a full circle would be \( A = \pi (15)^2 = \pi \cdot 225 \).

Since the sprinkler only covers a semicircle, we divide this area by 2:

\[ A = \frac{1}{2} \cdot 225\pi = 112.5\pi \text{ ft}^2 \]

Thus, the area that the sprinkler can spray is:

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

So the correct answer is:

A = 112.5π ft².