Question

The radius of a circle is 6 in. Find the area of a sector with an angle of 120°.(1 point) Responses A=12π in.2 upper A equals 12 pi in. squared A=2π in.2 upper A equals 2 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 formula:

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

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

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

First, calculate the area of the whole circle:

\[
\text{Area of the circle} = \pi r^2 = \pi (6^2) = 36\pi \text{ in}^2
\]

Now, apply the formula for the area of the sector:

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

Simplifying this:

\[
\text{Area of the sector} = \frac{1}{3} \times 36\pi = 12\pi \text{ in}^2
\]

Thus, the area of the sector with an angle of 120° is

\[
\boxed{12\pi \text{ in}^2}
\]