Answer:
[tex]1117.01 \mathrm{ft}^{2} \text { is the watered are by the sprinkler. }[/tex]
Option: A
Step-by-step explanation:
A sprinkler sprays water over a distance of (r) = 40 feet
Rotates through an angle of (θ) = 80°
80° convert to radians
[tex]\text { Radians }=80^{\circ} \times\left(\frac{\pi}{180}\right)[/tex]
[tex]\text { Radians }=80^{\circ} \times 0.017453292[/tex]
θ in Radians = 1.396263402
We know that,
Area of sprinkler is [tex]\mathrm{A}=\frac{1}{2} \mathrm{r}^{2} \theta[/tex]
Substitute the given values,
[tex]A=\frac{1}{2} \times 40^{2} \times 1.396263402[/tex]
[tex]A=\frac{(1600 \times 1.396263402)}{2}[/tex]
[tex]\mathrm{A}=\frac{2234.021443}{2}[/tex]
[tex]\mathrm{A}=1117.01 \mathrm{ft}^{2}[/tex]
Area of sprinkler is [tex]1117.01 \mathrm{ft}^{2}[/tex]
