Question

What is the area of the sector of a circle with a central angle of 216° and a radius of 7 inches? Leave your answer rounded to the nearest tenth. (1 point) Responses 13.2 inches 13.2 inches 26.4 inches 26.4 inches 92.4 inches 92.4 inches 29.4 inches

Answer 1

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

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

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

In this case, we have:
- \(\theta = 216^\circ\),
- \(r = 7\) inches.

Now, let's calculate the area of the sector:

1. Calculate \(r^2\):
\[
r^2 = 7^2 = 49
\]

2. Substitute \(r^2\) and \(\theta\) into the formula:
\[
\text{Area of sector} = \frac{216}{360} \times \pi \times 49
\]

3. Simplify \(\frac{216}{360}\):
\[
\frac{216}{360} = \frac{3}{5} = 0.6
\]

4. Now calculate the area:
\[
\text{Area of sector} = 0.6 \times \pi \times 49
\]
\[
\text{Area of sector} \approx 0.6 \times 3.14 \times 49 \approx 0.6 \times 153.86 \approx 92.316
\]

5. Round the area to the nearest tenth:
\[
\approx 92.3 \text{ square inches}
\]

Therefore, the area of the sector of the circle is approximately **92.4 inches** when rounded to the nearest tenth.