Question

What is the area of the sector of a circle with θ=216° and a radius of 7 inches? Express your answer in terms of pi.(1 point)
Responses

A=19.6π in.2
upper A equals 19.6 pi in. squared

A=29.4π in.2
upper A equals 29.4 pi in. squared

A=49π in.2
upper A equals 49 pi in. squared

A=4.2π in.2
upper A equals 4.2 pi in. squared

Answer 1

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

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

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:
- \(\theta = 216^\circ\),
- \(r = 7\) inches.

Plugging the values into the formula:

\[
A = \frac{216}{360} \times \pi \times 7^2
\]

Calculating \(7^2\):

\[
7^2 = 49
\]

Now substitute back in:

\[
A = \frac{216}{360} \times \pi \times 49
\]

Next, simplify \(\frac{216}{360}\):

\[
\frac{216}{360} = \frac{3}{5}
\]

Thus, the area becomes:

\[
A = \frac{3}{5} \times \pi \times 49 = \frac{147}{5} \pi
\]

Calculating \(\frac{147}{5}\):

\[
\frac{147}{5} = 29.4
\]

So, the area of the sector is:

\[
A = 29.4\pi
\]

Therefore, the correct response is:

**A = 29.4π in²**.