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 49π in2 49π in2 4.2π in2 4.2π in2 29.4π in2 29.4π in2 19.6π in2

Answer 1

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

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

where \(\theta\) is the angle in degrees and \(r\) is the radius.

Given:
- \(\theta = 216^\circ\)
- \(r = 7 \, \text{inches}\)

Now, substitute these values into the formula:

\[
\text{Area} = \frac{216}{360} \times \pi \times (7)^2
\]

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

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

Now, calculate \(7^2\):

\[
7^2 = 49
\]

Now, substitute this back into the area formula:

\[
\text{Area} = \frac{3}{5} \times \pi \times 49
\]

Calculating the area:

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

\(\frac{147}{5}\) can be simplified as:

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

So, the area is:

\[
29.4\pi \, \text{in}^2
\]

Thus, the area of the sector of the circle is \(\boxed{29.4\pi}\) in².