Question

A circle has radius of 6 ft. find the area of a sector if θ = 150. leave your answer in terms of pi

Answer 1

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

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

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

Given:
- \(r = 6\) ft,
- \(\theta = 150^\circ\).

Now, plug the values into the formula:

\[
\text{Area of a sector} = \frac{150}{360} \times \pi (6^2)
\]

Calculating \(6^2\):

\[
6^2 = 36
\]

Now substitute this value back into the formula:

\[
\text{Area of a sector} = \frac{150}{360} \times \pi \times 36
\]

Next, simplify \(\frac{150}{360}\):

\[
\frac{150}{360} = \frac{15}{36} = \frac{5}{12}
\]

Putting it all together:

\[
\text{Area of a sector} = \frac{5}{12} \times \pi \times 36
\]

Now multiply \(\frac{5}{12}\) by \(36\):

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

Thus, the area of the sector is:

\[
\text{Area of a sector} = 15\pi \text{ ft}^2
\]

Therefore, the area of the sector is \(\boxed{15\pi}\) ft².