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

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

A=2π 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,
- \( r \) is the radius of the circle.

Given:
- \( r = 6 \) inches,
- \( \theta = 120^\circ \).

Now, substitute the values into the formula:

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

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

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

Next, calculate \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substitute back into the area formula:

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

\[
A = 12\pi
\]

Therefore, the area of the sector is \( 12\pi \) square inches.

The correct response is:
**A = 12π in²**