Question

Find the area of a sector for a circle with a radius of 12 feet and a central angle of 270°. Round your answer to the nearest tenth.(1 point) Responses 339.3 ft² 339.3 ft² 56.5 ft² 56.5 ft² 19.6 ft² 19.6 ft² 452.4 ft²

Answer 1

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

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

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

Given:
- \(r = 12\) feet
- \(\theta = 270^\circ\)

Plugging the values into the formula:

\[
\text{Area of sector} = \frac{270}{360} \times \pi \times (12)^2
\]

Calculating the fraction:

\[
\frac{270}{360} = \frac{3}{4}
\]

Now, calculating \( (12)^2 \):

\[
(12)^2 = 144
\]

Now, substituting back into the formula:

\[
\text{Area of sector} = \frac{3}{4} \times \pi \times 144
\]

Calculating \(\frac{3}{4} \times 144\):

\[
\frac{3 \times 144}{4} = 108
\]

So,

\[
\text{Area of sector} = 108\pi
\]

Now, using \(\pi \approx 3.14\):

\[
\text{Area of sector} \approx 108 \times 3.14 = 339.12
\]

Rounding to the nearest tenth, the area of the sector is approximately:

\[
\text{Area of sector} \approx 339.1\ \text{ft}^2
\]

Among the provided options, the closest answer is:

**339.3 ft².**