Question

The radius of a circle is 6 in. Find the area of a sector with an angle of 120°.(1 point)
Responses

A=2π in.2
upper A equals 2 pi in. squared

A=12π in.2
upper A equals 12 pi in. squared

A=36π in.2
upper A equals 36 pi in. squared

A=9π in.2

Answer 1

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

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

where \(\theta\) is the angle of the sector in degrees and \(r\) is the radius of the circle.

Given:
- Radius \(r = 6\) inches
- Angle \(\theta = 120^\circ\)

Now plug these values into the formula:

\[
\text{Area of sector} = \frac{120}{360} \times \pi (6^2)
\]

First, calculate \(6^2\):

\[
6^2 = 36
\]

Now substitute that value into the formula:

\[
\text{Area of sector} = \frac{120}{360} \times \pi \times 36
\]

Next, simplify \(\frac{120}{360}\):

\[
\frac{120}{360} = \frac{1}{3}
\]

Now, substitute back into the equation:

\[
\text{Area of sector} = \frac{1}{3} \times \pi \times 36
\]

Now multiply:

\[
\text{Area of sector} = \frac{36\pi}{3} = 12\pi
\]

Thus, the area of the sector is:

\[
A = 12\pi \text{ in}^2
\]

The correct response is:

**A = 12π in²**