Question

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

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

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

Answer 1

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

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

where \(A\) is the area, \(\theta\) is the central angle in degrees, and \(r\) is the radius.

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

Now we can plug in the values into the formula:

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

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

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

Now substitute back into the formula:

\[
A = \frac{1}{3} \times \pi \times 36
\]

Calculating \( \pi \times 36 \):

\[
A = \frac{1}{3} \times 36\pi = 12\pi
\]

So, the area of the sector is:

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

Thus, the correct response is:

**A = 12π in²**