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=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:

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