Question

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

a. A = 12π in.^2
b. A = 36π in.^2
c. A = 9π in.^2
d. A = 2π 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 of the sector,
- \( \theta \) is the central angle in degrees,
- \( r \) is the radius of the circle.

In this case, the radius \( r \) is 6 inches, and the angle \( \theta \) is 120°.

Plugging in the values, we get:

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

Calculating \( 6^2 \):

\[
6^2 = 36
\]

Now substitute \( 36 \) into the formula:

\[
A = \frac{120}{360} \times \pi \times 36
\]

Simplifying \( \frac{120}{360} \):

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

Thus, the area becomes:

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

So, the area of the sector is:

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

The correct answer is:

**a. \( A = 12\pi \text{ in}^2 \)**.