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=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

Answer 1

To find the area that the sprinkler can spray, we need to consider that it operates over a half-circle (180°) with a radius of 15 feet.

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

\[ A = \pi r^2 \]

Since the sprinkler only sprays over half of a circle, we will take half of this area.

1. Calculate the area of a full circle with radius 15 feet:

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

2. To find the area for a half-circle:

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

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

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