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

Question

Responses

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

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

A=9π in.2
upper A equals 9 pi in. squared

A=36π in.2

Answer 1

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

$$A=\frac{\theta }{360}\times \pi r^2$$

where $A$ is the area of the sector, $\theta$ is the angle of the sector in degrees, and $r$ is the radius of the circle.

In this case:

• The radius $r=6$ in.
• The angle $\theta ={120}^{\circ }$.

Now plug the values into the formula:

$$A=\frac{120}{360}\times \pi (6{)}^2$$

Calculating this step by step:

1. Calculate $\frac{120}{360}=\frac{1}{3}$.
2. Calculate $(6{)}^2=36$.
3. Now substitute these values back into the formula:

$$A=\frac{1}{3}\times \pi \times 36$$

4. Simplify:

$$A=\frac{36\pi }{3}=12\pi$$

Thus, the area of the sector is:

$$\boxed{{\displaystyle 12\pi {\text{ in}}^2}}$$