Question

What is the area of the sector of a circle with a central angle of 168° and a radius of 15 inches? Leave your answer rounded to the nearest tenth. (1 point) Responses 22.0 inches 22.0 inches 329.9 inches 329.9 inches 44.0 inches 44.0 inches 659.7 inches

Answer 1

To find the area of a sector of a circle, you can use the formula:

\[
\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2
\]

where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.

In this case:
- \(\theta = 168^\circ\),
- \(r = 15\) inches.

Let's compute the area:

1. First, calculate \( \pi r^2 \):
\[
\pi r^2 = \pi (15)^2 = \pi \times 225 = 225\pi
\]

2. Now, find the area of the sector:
\[
\text{Area} = \frac{168}{360} \times 225\pi
\]

3. Simplifying \( \frac{168}{360} \):
\[
\frac{168}{360} = \frac{14}{30} = \frac{7}{15}
\]

4. Now substitute back into the area formula:
\[
\text{Area} = \frac{7}{15} \times 225\pi = 105\pi
\]

5. To find the numerical value of the area, use \( \pi \approx 3.14 \):
\[
\text{Area} \approx 105 \times 3.14 = 329.7
\]

Finally, rounding to the nearest tenth:
\[
\text{Area} \approx 329.7 \text{ inches}^2
\]

Thus, the area of the sector is **329.9 inches²** when rounded to the nearest tenth.