Question

the sector shows the area of a lawn that will be watered by a sprinkler. what is the area, rounded to the nearest tenth? use 3.14 for π. 10 ft 30° 191.1 square feet 26.2 square feet 5.2 square feet 95.5 square feet

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle.

Step2: Identify values of $\theta$ and $r$

From the problem, $\theta = 30^{\circ}$ and $r = 10$ ft.

Step3: Substitute values into the formula

$A=\frac{30^{\circ}}{360^{\circ}}\times3.14\times(10)^{2}$.
First, simplify $\frac{30^{\circ}}{360^{\circ}}=\frac{1}{12}$. Then, $(10)^{2}=100$. So, $A=\frac{1}{12}\times3.14\times100$.

Step4: Calculate the area

$A=\frac{314}{12}\approx26.2$ square feet.

Answer:

26.2 square feet