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:

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

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.

For this problem:

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

Now, plug in the values into the formula:

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

First, calculate $(6{)}^2$: $$(6{)}^2=36$$

Now, substitute $36$ into the formula: $$A=\frac{120}{360}\times \pi \times 36$$

Simplify $\frac{120}{360}$: $$\frac{120}{360}=\frac{1}{3}$$

Now, substitute back into the formula: $$A=\frac{1}{3}\times \pi \times 36$$

Now, multiply $\frac{1}{3}$ by $36$: $$A=12\pi$$

Thus, the area of the sector is: $$\boxed{{\displaystyle 12\pi {\text{ in}}^2}}$$