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. image of a sector with radius 10 ft and central angle 30° options: 26.2 square feet, 96.5 square feet, 191.1 square feet, 5.2 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 in degrees and $r$ is the radius of the circle.

Step2: Identify values

Here, $\theta = 30^\circ$, $r = 10$ ft, and $\pi = 3.14$.

Step3: Substitute into formula

First, calculate $r^2$: $r^2 = 10^2 = 100$. Then, calculate $\frac{\theta}{360^\circ}$: $\frac{30^\circ}{360^\circ} = \frac{1}{12}$. Now, substitute into the area formula: $A = \frac{1}{12} \times 3.14 \times 100$.

Step4: Perform calculation

First, multiply $3.14$ and $100$: $3.14 \times 100 = 314$. Then, divide by $12$: $\frac{314}{12} \approx 26.17$. Rounding to the nearest tenth gives approximately $26.2$. Wait, but let's check again. Wait, maybe I made a mistake. Wait, $30/360 = 1/12$, $1/12 * 3.14 * 100 = (314)/12 ≈ 26.166...$, which is approximately $26.2$ square feet. Wait, but the options include 26.2 square feet. Wait, but let me check the problem again. Wait, the radius is 10 ft, central angle 30 degrees. So sector area is (30/360)π10² = (1/12)3.14100 = 314/12 ≈26.17, which is 26.2 when rounded to the nearest tenth.

Answer:

26.2 square feet