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

Question

Responses

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

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

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

A=12π 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 in degrees, and \( r \) is the radius of the circle.

In this case, the radius \( r = 6 \) inches and the angle \( \theta = 120^\circ \).

Now, plug in the values:

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

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

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

Now calculate \( \pi (6)^2 \):

\[ (6)^2 = 36 \Rightarrow \pi (6)^2 = 36\pi \]

Now substitute back into the formula:

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

Therefore, the area of the sector is

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

So the correct response is:

A = 12π in.².