Question

A circle has a radius of 6 ft. Find the area of a sector if θ=150° . Leave your answer in terms of π .(1 point) A= π ft.2

Answer 1

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

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

Where:
- \(A\) is the area of the sector,
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.

Given:
- \(r = 6 \text{ ft}\)
- \(\theta = 150^\circ\)

Substituting the given values into the formula:

\[
A = \frac{150^\circ}{360^\circ} \times \pi (6)^2
\]

Calculating \(6^2\):

\[
6^2 = 36
\]

Now substituting that back into the area formula:

\[
A = \frac{150}{360} \times \pi \times 36
\]

Simplifying \(\frac{150}{360}\):

\[
\frac{150}{360} = \frac{5}{12}
\]

Now, substituting:

\[
A = \frac{5}{12} \times \pi \times 36
\]

Calculating \( \frac{5}{12} \times 36\):

\[
\frac{5 \times 36}{12} = \frac{180}{12} = 15
\]

So, the area of the sector is:

\[
A = 15\pi \text{ ft}^2
\]

Thus, the final answer is:

\[
\boxed{15\pi \text{ ft}^2}
\]