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

A=112.5π ft.2

Answer 1

To find the area sprayed by the sprinkler, we first note that the sprinkler activates over a semicircular area since it rotates 180°. The radius of this semicircular area is the distance the water can be thrown, which is 15 feet.

The area \( A \) of a full circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius. For a semicircle, the area will be half of that:

\[ A = \frac{1}{2} \pi r^2 \]

Now, substituting the radius given (15 feet):

\[ A = \frac{1}{2} \pi (15)^2 \] \[ A = \frac{1}{2} \pi (225) \] \[ A = \frac{225}{2} \pi \] \[ A = 112.5 \pi \text{ ft}^2 \]

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

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